Method for determing a commutation offset and for determining a compensation map for a stage

ABSTRACT

A method for determining a commutation offset for a mover ( 250 A) of a mover assembly ( 220 C) that moves and positions a stage ( 220 A) relative to a stage base ( 220 B) includes controlling the mover assembly ( 220 C) in a closed loop fashion to maintain the position of the stage ( 220 A) along a first axis and along a second axis with the stage ( 220 A) levitated above the stage base ( 220 B). The method also includes the steps of (i) directing current to a coil array ( 240 ) of the mover assembly ( 220 C) so that the mover assembly ( 220 C) imparts a disturbance on the stage ( 220 A); and (ii) evaluating one or more forces generated by the mover assembly ( 220 C) as a result of the disturbance on the stage ( 220 A) created by the mover ( 250 A). Further, a method for generating a compensation map ( 1402 ) includes sequentially directing a plurality of excitation signals to the control of the mover assembly ( 220 C) and determining the control commands that result from the plurality of excitation signals.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.13/101,264 filed on May 5, 2011 and entitled “METHOD FOR DETERMINING ACOMMUTATION OFFSET AND FOR DETERMINING A COMPENSATION MAP FOR A STAGE”which is currently pending. This application claims priority onProvisional Application Ser. No. 61/345,988 filed on May 18, 2010,entitled “METHODS TO FIND THE COMMUTATION OFFSET OF A TWO DEGREE OFFREEDOM ACTUATOR” and on Provisional Application Ser. No. 61/363,806filed on Jul. 13, 2010, entitled “METHOD FOR DETERMINING COMMUTATIONOFFSET”. As far as is permitted, the contents of U.S. application Ser.No. 13/101,264, and Provisional Application Ser. Nos. 61/345,988 and61/363,806 are incorporated herein by reference.

BACKGROUND

Exposure apparatuses are commonly used to transfer images from a reticleonto a semiconductor wafer during semiconductor processing. A typicalexposure apparatus includes an illumination source, a reticle stageassembly that positions a reticle, an optical assembly having an opticalaxis, a wafer stage assembly that positions a semiconductor wafer, ameasurement system, and a control system. Each stage assembly includesone or more movers, and each of the movers includes a coil array thatinteracts with a magnet assembly. The measurement system constantlymonitors the position of the reticle and the wafer, and the controlsystem controls each stage assembly to constantly adjust the position ofthe reticle and the wafer. The features of the images transferred fromthe reticle onto the wafer are extremely small. Accordingly, the precisepositioning of the wafer and the reticle is critical to themanufacturing of high quality wafers.

In certain designs, the position of the respective stage measured by themeasurement system is not an absolute position, but instead is relativeto where the stage assembly happens to be when the measurement system isinitialized. Therefore, it is imperative to determine an offset valuethat aligns the measured interferometer position to the actual poles ofthe magnet assembly for proper commutation of the movers. This offsetvalue is often called the “commutation offset”.

The amount of force generated by each mover is a sinusoidal function ofhow accurately the commutation offset value is determined. For example,if the error between the calculated and real commutation offset is threepercent, then the force generated by the mover is approximatelyninety-eight percent of the maximum possible (and expected) force.However, for a commutation error of seven percent, the force falls toapproximately ninety percent. Thus, it is important to accuratelydetermine the commutation offset for each mover so that each moveroperates efficiently and accurately.

SUMMARY

The present invention is directed to a method for determining acommutation offset for a mover of a mover assembly that moves andpositions a stage relative to a stage base. In one embodiment, the movergenerates a first axis force that moves and positions the stage along afirst axis, and a second axis force that moves and positions the stagealong a vertically oriented second axis that is orthogonal to the firstaxis. Further, the mover includes a coil array. The method includescontrolling the mover assembly in a closed loop fashion to maintain theposition of the stage along the first axis and along the second axiswith the stage levitated above the stage base. Additionally, the methodincludes determining a first commutation offset for the mover. This stepcan include (i) directing current to the coil array so that the moverimparts a disturbance on the stage, and (ii) evaluating one or moreforces generated by the mover assembly as a result of the disturbance onthe stage created by the mover.

With some of the methods provided herein, the stage is levitated duringthe commutation procedure. As a result thereof, the present method canbe used for a planar or linear motor arrangement such as a magneticlevitation (“maglev”) type stage, which does not have redundant moversthat generate forces along the second axis.

The present invention is also directed to a control system fordetermining a commutation offset for a mover of a mover assembly. Thepresent invention is additionally directed to a stage assembly thatmoves a work piece, the stage assembly including a stage that retainsthe work piece and a mover in which the commutation offset is determinedutilizing one of the methods provided herein. In yet another embodiment,the present invention is directed to an exposure apparatus that includesan illumination system and a stage assembly that moves the stagerelative to the illumination system. In still another embodiment, thepresent invention is directed to a process for manufacturing a devicethat includes the steps of providing a substrate and forming an image tothe substrate with the exposure apparatus.

In still another embodiment, the present invention is directed to amethod for controlling a mover assembly that includes the steps of:controlling the mover assembly with a control system to position thestage at a first test position; applying a first excitation signal withthe control system to the mover assembly with the stage at the firsttest position; and determining a first set of control commands for thefirst excitation signal. In this embodiment, a second excitation signalcan be applied to the mover assembly with the stage at the first testposition, and a second set of control commands for the second excitationsignal can be determined. Further, in this embodiment, the moverassembly can be controlled with the control system utilizing informationfrom the sets of control commands.

Additionally, the method can include the steps of generating acompensation map from the first set of control commands and the secondset of control commands, and controlling the mover assembly with thecontrol system utilizing information from the compensation map.

Moreover, the present invention is directed to a mover assembly thatmoves and positions a stage relative to a stage base, the mover assemblycomprising: a mover that moves and positions the stage relative to thestage base; and a control system that controls the mover, the controlsystem (i) directing current to the mover to position the stage at afirst test position; (ii) applying a first excitation signal to themover with the stage at the first test position; and (iii) determining afirst set of control commands for the first excitation signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of this invention, as well as the invention itself,both as to its structure and its operation, will be best understood fromthe accompanying drawings, taken in conjunction with the accompanyingdescription, in which similar reference characters refer to similarparts, and in which:

FIG. 1 is a schematic illustration of an exposure apparatus havingfeatures of the present invention;

FIG. 2A is a simplified top perspective illustration of a mover assemblyhaving features of the present invention;

FIG. 2B is a simplified view of a portion of the mover assembly of FIG.2A;

FIG. 3 is a simplified schematic of a control system that can be used tocontrol the mover assembly of FIG. 2A;

FIG. 4A is a flow chart that illustrates a first process that can beused to estimate the commutation offsets for the mover assembly of FIG.2A;

FIG. 4B is a simplified illustration of how force commands vary relativeto possible commutation offsets;

FIG. 5A is a flow chart that illustrates another process that can beused to estimate the commutation offsets for the mover assembly of FIG.2A;

FIG. 5B is a simplified illustration of how force commands vary relativeto possible commutation offsets;

FIG. 6 is a simplified schematic of another embodiment of control systemthat can be used to control the mover assembly of FIG. 2A;

FIG. 7 is a flow chart that illustrates yet another process that can beused to estimate the commutation offsets for the mover assembly of FIG.2A;

FIG. 8A is a graph that illustrates test force versus time;

FIG. 8B is a graph that illustrates test offset versus time;

FIG. 8C is a graph that illustrates current commands versus time;

FIG. 8D is a graph that illustrates X axis force versus test offset;

FIG. 8E is a graph that illustrates Z axis force versus test offset;

FIG. 8F is a graph that illustrates Y axis force versus test offset;

FIG. 8G is a graph that illustrates X axis force versus test offset fora plurality of alternative positions;

FIG. 8H is a graph that illustrates Z axis force versus test offset fora plurality of alternative positions;

FIG. 8I is a graph that illustrates X axis force versus test offset fora plurality of alternative positions;

FIG. 8J is a graph that illustrates Z axis force versus test offset fora plurality of alternative positions;

FIG. 9 is a flow chart that illustrates one method of generating acompensation map having features of the present invention;

FIG. 10A is a simplified view of a plurality of test positions havingfeatures of the present invention;

FIG. 10B illustrates position versus time for an excitation signal;

FIG. 10C illustrates acceleration versus time for an excitation signal;

FIG. 11A is a graph that illustrates a plurality of excitation signalsversus time;

FIGS. 11B-11G illustrate following errors versus time that result fromthe excitation signals;

FIGS. 11H-11M illustrate control commands versus time;

FIG. 12 is a simplified schematic of another embodiment of controlsystem that can be used to generate a compensation map;

FIGS. 13A-13F illustrate compensation ratios versus a plurality of testpositions;

FIG. 14A is a simplified illustration of a compensation map;

FIG. 14B is an enlarged illustration of a portion of the compensationmap of FIG. 14A;

FIG. 15A is a simplified schematic of another embodiment of controlsystem that can be used to control the mover assembly;

FIG. 15B is a simplified illustration of a six by six force compensationmatrix;

FIG. 16 is a simplified graph that illustrates position versus time;

FIGS. 17A-17F are simplified graphs that illustrate following errorversus time;

FIG. 18A is a map that illustrates the residual force compensationratios with the application of the center of gravity force compensation;

FIG. 18B is an enlarged illustration of a portion of the map of FIG.18A;

FIG. 19A is a flow chart that outlines a process for manufacturing adevice in accordance with the present invention; and

FIG. 19B is a flow chart that outlines device processing in more detail.

DESCRIPTION

FIG. 1 is a schematic illustration of a precision assembly, namely anexposure apparatus 10 having features of the present invention. Theexposure apparatus 10 includes an apparatus frame 12, an illuminationsystem 14 (irradiation apparatus), an optical assembly 16, a reticlestage assembly 18, a wafer stage assembly 20, a measurement system 22,and a control system 24. The design of the components of the exposureapparatus 10 can be varied to suit the design requirements of theexposure apparatus 10. The exposure apparatus 10 is particularly usefulas a lithographic device that transfers a pattern (not shown) of anintegrated circuit from a reticle 26 onto a semiconductor wafer 28. Theexposure apparatus 10 mounts to a mounting base 30, e.g., the ground, abase, or floor or some other supporting structure.

As an overview, in certain embodiments, the control system 24 disclosedherein utilizes one or more unique methods to determine commutationoffsets for the movers of one or both of the stage assemblies 18, 20with improved accuracy. Further, in certain embodiments, the controlsystem 24 disclosed herein utilizes one or more other compensationmethods that improve the positioning of the respective stage assemblies18, 20. As a result thereof, the wafer 28 and/or the reticle 26 can bepositioned with improved accuracy, and the stage assemblies 18, 20 canbe operated more efficiently. This can result in the manufacturing ofhigher density wafers 28 with the exposure apparatus 10.

A number of Figures include an orientation system that illustrates an Xaxis, a Y axis that is orthogonal to the X axis, and the Z axis that isorthogonal to the X and Y axes. It should be noted that any of theseaxes can also be referred to as the first, second, and/or third axes.

There are a number of different types of lithographic devices. Forexample, the exposure apparatus 10 can be used as a scanning typephotolithography system. Alternatively, the exposure apparatus 10 can bea step-and-repeat type photolithography system. However, the use of theexposure apparatus 10 provided herein is not limited to aphotolithography system for semiconductor manufacturing. The exposureapparatus 10, for example, can be used as an LCD photolithography systemthat exposes a liquid crystal display device pattern onto a rectangularglass plate or a photolithography system for manufacturing a thin filmmagnetic head.

The apparatus frame 12 is rigid and supports the components of theexposure apparatus 10. The apparatus frame 12 illustrated in FIG. 1supports the reticle stage assembly 18, the optical assembly 16, and theillumination system 14 above the mounting base 30.

The illumination system 14 includes an illumination source 32 and anillumination optical assembly 34. The illumination source 32 emits abeam (irradiation) of light energy. The illumination optical assembly 34guides the beam of light energy from the illumination source 32 to theoptical assembly 16. The illumination source 32 can be a g-line source(436 nm), an i-line source (365 nm), a KrF excimer laser (248 nm), anArF excimer laser (193 nm), a F₂ laser (157 nm), or an EUV source (13.5nm). Alternatively, the illumination source 32 can generate chargedparticle beams such as an x-ray or an electron beam.

The optical assembly 16 projects and/or focuses the light leaving thereticle 26 to the wafer 28. Depending upon the design of the exposureapparatus 10, the optical assembly 16 can magnify or reduce the imageilluminated on the reticle 26.

The reticle stage assembly 18 holds and positions the reticle 26relative to the optical assembly 16 and the wafer 28. In FIG. 1, thereticle stage assembly 18 includes a reticle stage 18A that retains thereticle 26, a reticle stage base 18B, and a reticle stage mover assembly18C that positions the reticle stage 18A and the reticle 26. The reticlestage mover assembly 18B can be designed to move the reticle 26 with sixdegrees of freedom (X, Y, and Z axes, and about X, Y, and Z axes)relative to the reticle stage base 18B. In alternate embodiments, thereticle stage mover assembly 18B can be designed to move the reticle 26with one (Y axis) or three (X and Y axes, and about Z axis) degrees offreedom.

Somewhat similarly, the wafer stage assembly 20 holds and positions thewafer 28 with respect to the projected image of the illuminated portionsof the reticle 26. In FIG. 1, the wafer stage assembly 20 includes awafer stage 20A that retains the wafer 28, a wafer stage base 20B, and awafer stage mover assembly 20C that positions the wafer stage 20A andthe wafer 28. The wafer stage mover assembly 20C can be designed to movethe wafer 28 with up to six degrees of freedom (along the X, Y, and Zaxes, and about X, Y, and Z axes) relative to the wafer stage base 20B.

The measurement system 22 monitors movement of the reticle 26 and thewafer 28 relative to the optical assembly 16 or some other reference.With this information, the apparatus control system 24 can control thereticle stage assembly 18 to precisely position the reticle 26 and thewafer stage assembly 20 to precisely position the wafer 28. For example,the measurement system 22 can utilize multiple laser interferometers,encoders, autofocus systems, and/or other measuring devices. In FIG. 1,the measurement system 22 includes (i) a reticle measurement system 22A(illustrated as a box) that monitors the position of the reticle stage18B and the reticle 26, and (ii) a wafer measurement system 22B(illustrated as a box) that monitors the position of the wafer stage20A.

The control system 24 is connected to the reticle stage assembly 18, thewafer stage assembly 20, and the measurement system 22. The assemblycontrol system 24 receives information from the measurement system 22and controls the stage assemblies 18, 20 to precisely position thereticle 26 and the wafer 28. The assembly control system 24 can includeone or more processors and circuits.

FIG. 2A is a simplified schematic illustration of a control system 224,and a stage assembly 220 that positions a work piece 200 (illustratedabove the stage assembly 220) with improved accuracy and improvedefficiency. In one embodiment, the work piece 200 can be the wafer 28(illustrated in FIG. 1) and the stage assembly 220 can be used as thewafer stage assembly 22. Alternatively, the stage assembly 220 can beused to move and position other types of work pieces 200 (e.g. thereticle 26 illustrated in FIG. 1) during manufacturing and/orinspection.

In FIG. 2A, the stage assembly 220 includes a stage 220A, a stage base220B, and a stage mover assembly 220C. The design of these componentscan be varied to suit the requirements of the stage assembly 220. Thestage 220A selectively retains the work piece 200. For example, thestage 220A can include a chuck for selectively retaining the work piece200. The stage base 220B supports a portion of the stage mover assembly220C. In FIG. 2A, the stage 220A is a rigid, generally rectangularshaped plate, and the stage base 220B is also a rigid, generallyrectangular shaped plate.

The stage mover assembly 220C moves the stage 220A and the work piece200 relative to the stage base 220B. In FIG. 2A, the stage moverassembly 220C is designed to move the stage 220A with six degrees offreedom, namely along the X axis, along the Y axis, along the Z axis,about the X axis (theta X (Tx)), about the Y axis (theta Y (Ty)), andabout the Z axis (theta Z (Tz)). Alternatively, the stage mover assembly220C can be designed to move the stage 220A with fewer than six degreesof freedom.

In FIG. 2A, the stage mover assembly 220C includes a coil assembly 236that is fixed to and moves with the stage 220A, and a magnet assembly238 that is fixed to the stage base 220B that cooperate to define aplanar motor. In this embodiment, the coil assembly 236 includes a firstYZ coil array 240, a second YZ coil array 242, a first XZ coil array244, and a second XZ coil array 246. In this embodiment, the stage 220Acan be divided into four quadrants, and one of the coil arrays 240, 242,244, 246 is secured to each of the quadrants. More specifically, in thisembodiment, (i) the first XZ coil array 244 is secured to a right frontquadrant of the stage 220A; (ii) the first YZ coil array 240 is securedto a right rear quadrant of the stage 220A; (iii) the second YZ coilarray 242 is secured to a left front quadrant of the stage 220A; and(iv) the second XZ coil array 246 is secured to a left rear quadrant ofthe stage 220A. Moreover, in this embodiment, the YZ coil arrays 240,242 are oriented so that their coil wires are aligned perpendicular tothe Y axis, and the XZ coil arrays 244, 246 are oriented so that theircoil wires are aligned perpendicular to the X axis. Alternatively, thearrangement of the coil arrays 240, 242, 244, 246 can be different thanthat illustrated in FIG. 2A.

As provided herein, each coil array 240, 242, 244, 246 includes one ormore coils 248. In FIG. 2A, the stage mover assembly 220C includes four,three phase motors. Thus, each coil array 240, 242, 244, 246 includes amultiple of three coils 248. In the simplified example illustrated inFIG. 2A, each of the coil arrays 240, 242, 244, 246 includes threepartly overlapping coils 248. For each coil array 240, 242, 244, 246,(i) one of the coils 248 can be referred to as the U phase coil; (ii)one of the coils 248 can be referred to as the V phase coil; and (iii)one of the coils 248 can be referred to as the W phase coil. A suitablecoil array is described in detail in U.S. Pat. No. 6,208,045 and U.S.Pat. No. 7,205,741 B1, the contents of which are incorporated herein byreference. Alternatively, for example, each coil array 240, 242, 244,246 can be a two phase system that includes a multiple of two coils 248.

Further, in FIG. 2A, the coil arrays 240, 242, 244, 246 are designed andpositioned (i) so that current can be directed to the first YZ coilarray 240 and the second YZ coil array 242 to create forces on the stagealong the Y axis and along the Z axis; and (ii) so that current can bedirected to the first XZ coil array 244 and the second XZ coil array 246to create forces on the stage 220A along the X axis and along the Zaxis. With this design, (i) the first YZ coil array 240 cooperates withthe magnet array 238 to define a first YZ mover 250A that generates afirst Y axis force (oriented along the Y axis) that moves the stage 220Aalong the Y axis, and that generates a first Z axis force (orientedalong the Z) that moves the stage 220A along the Z axis; (ii) the secondYZ coil array 242 cooperates with the magnet array 238 to define asecond YZ mover 250B that generates a second Y axis force (orientedalong the Y axis) that moves the stage 220A along the Y axis, and thatgenerates a second Z axis force (oriented along the Z axis) that movesthe stage 220A along the Z along the Z axis; (iii) the first XZ coilarray 244 cooperates with the magnet array 238 to define a first XZmover 250C that generates a first X axis force (oriented along the Xaxis) that moves the stage 220A along the X axis, and that generates athird Z axis force (oriented along the Z) that moves the stage 220Aalong the Z axis; and (iv) the second XZ coil array 246 cooperates withthe magnet array 238 to define a second XZ mover 250D that generates asecond X axis force (oriented with the X axis) that moves the stage 220Aalong the X axis, and that generates a fourth Z axis force (orientedwith the Z axis) that moves the stage 220A along the Z axis.

It should be noted that any of the X, Y, or Z axis forces canalternatively be referred to as a first axis force, a second axis force,or a third axis force.

Moreover, in FIG. 2A, the magnet assembly 238 includes a two dimensionalarray (orientated along the X and Y axes) of magnets 251 that aresecured to the stage base 220B. In one non-exclusive embodiment, themagnets 251 are configured in a checkerboard pattern with a plurality ofrows in the X direction, and a plurality of columns in the Y direction.In this embodiment, the polar axes of all magnets 251 in the array 38are aligned parallel to the Z direction (perpendicular to the X-Ycoordinate plane). Alternatively, for example, the magnets 251 can bearranged so that the rows are at an angle (e.g. forty-five degrees)relative to the X direction, and the columns are at an angle (e.g.forty-five degrees) relative to the Y direction.

Further, in FIG. 2A, the magnets 251 within any row or column have thesame polarity. For example, all of the magnets 251 in right most columnhave the S pole facing upward (labeled with an “S”), and all of themagnets 251 in second to the right most column have the N pole facingupward (labeled with an “N”). In FIG. 2A, there are twelve rows ofmagnets 251 and fifteen columns of magnets 251. In some embodiments,particularly those involving moving coil motors, the numbers of rows andcolumns in a magnetic assembly 238 are substantially larger, providingfor a larger desired range of travel. In this embodiment, the magnets251 are all equal in size and square in cross-section, although magnets251 of other shapes are also possible.

In an alternative embodiment, the stage mover assembly can be designedso that the coil assembly 236 is fixed to the stage base 220B and themagnet assembly 238 is secured to and moves with the stage 220A.Alternatively or additionally, the stage mover assembly can include oneor more linear motors or another type of mover.

In this embodiment, the control system 224 independently andconcurrently directs a different current to the each of the three (U, V,W) phase coils 248 for each of the coil arrays 240, 242, 244, 246 toprecisely position the work piece 200 and the stage 220A. Stated inanother fashion, in this embodiment, the control system 224 directs athree phase commutated electric current to the each of the coil arrays240, 242, 244, 246. With this design, the coil arrays 240, 242, 244, 246are powered to move relative to the stationary magnet assembly 238.Alternatively, the stage mover assembly 220C can be designed so that themagnet assembly 238 moves relative to stationary coil arrays 240, 242,244, 246. The control system 224 can include one or more processors thatare programmed to perform the steps provided herein.

In one embodiment, to control the first YZ mover 250A, the controlsystem 224 utilizes the following motor commutations to determine thecurrent to be directed to the different phases of the first YZ coilarray 240:

$\begin{matrix}{{\begin{pmatrix}I_{u,{{YZ}\; 1}} \\I_{v,{{YZ}\; 1}} \\I_{w,{{YZ}\; 1}}\end{pmatrix} = {\begin{pmatrix}{\sin \left( {2{\pi \cdot \frac{y + y_{o,{{YZ}\; 1}}}{L}}} \right)} & {\cos \left( {2{\pi \cdot \frac{y + y_{o,{{YZ}\; 1}}}{L}}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{o,{{YZ}\; 1}}}{L}}} + \frac{2\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{y + y_{o,{{YZ}\; 1}}}{L}}} + \frac{2\pi}{3}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{o,{{YZ}\; 1}}}{L}}} + \frac{4\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{y + y_{o,{{YZ}\; 1}}}{L}}} + \frac{4\pi}{3}} \right)}\end{pmatrix} \cdot \begin{pmatrix}A_{y,{{YZ}\; 1}} \\A_{z,{{YZ}\; 1}}\end{pmatrix}}}\mspace{79mu} {A_{y,{{YZ}\; 1}} = \frac{F_{Y\; 1}}{k_{y,{{YZ}\; 1}}}}\mspace{79mu} {A_{z,{{YZ}\; 1}} = \frac{F_{Z\; 1}}{k_{z,{{YZ}\; 1}}}}} & {{Equation}\mspace{14mu} (1)}\end{matrix}$

For the first YZ coil array 240, Equation (1) is the motor commutationformula, used to determine the current commands I_(u,YZ1), I_(v,YZ1),and I_(w,YZ1) directed to U, V, W phase coils respectively. Further, inEquation (1), (i) y is the present measured position along the Y axis ofthe coil assembly 236 (e.g. as measured with the measurement system 22illustrated in FIG. 1); (H) y_(o,YZ1) is the commutation offset of thefirst YZ coil array 240; (iii) k_(y,YZ1) and k_(z,YZ1) are the motorforce constants along Y and Z axis of the first YZ mover 250A, (iv)F_(Y1) and F_(Z1) are the motor force commands along the Y and Z axes ofthe first YZ mover 250A, determined by the control system 224, (v)A_(y,ZY1) and A_(z,ZY1) are the required current amplitudes required toproduce the desired force along Y and Z axes respectively for the firstYZ mover 250A and (vi) L is the associated motor commutation pitch.

Somewhat similarly, to control the second YZ mover 250B, the controlsystem 224 utilizes the following motor commutations to determine themagnitude of the current to be directed to the U, V, W phases of thesecond YZ coil array 242:

$\begin{matrix}{{\begin{pmatrix}I_{u,{{YZ}\; 2}} \\I_{v,{{YZ}\; 2}} \\I_{w,{{YZ}\; 2}}\end{pmatrix} = {\begin{pmatrix}{\sin \left( {2{\pi \cdot \frac{y + y_{o,{{YZ}\; 2}}}{L}}} \right)} & {\cos \left( {2{\pi \cdot \frac{y + y_{o,{{YZ}\; 2}}}{L}}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{o,{{YZ}\; 2}}}{L}}} + \frac{2\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{y + y_{o,{{YZ}\; 2}}}{L}}} + \frac{2\pi}{3}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{o,{{YZ}\; 2}}}{L}}} + \frac{4\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{y + y_{o,{{YZ}\; 2}}}{L}}} + \frac{4\pi}{3}} \right)}\end{pmatrix} \cdot \begin{pmatrix}A_{y,{{YZ}\; 2}} \\A_{z,{{YZ}\; 2}}\end{pmatrix}}}\mspace{79mu} {A_{y,{{YZ}\; 2}} = \frac{F_{Y\; 2}}{k_{y,{{YZ}\; 2}}}}\mspace{79mu} {A_{z,{{YZ}\; 2}} = \frac{F_{Z\; 2}}{k_{z,{{YZ}\; 2}}}}} & {{Equation}\mspace{14mu} (2)}\end{matrix}$

For the second YZ coil array 242, Equation (2) is the motor commutationformula, used to determine the current commands I_(u,YZ2), I_(v,YZ2),and I_(w,YZ2) directed to U, V, W phase coils respectively. Further, inEquation (2), (i) y is the present measured position along the Y axis ofthe coil assembly 236 (e.g. as measured with the measurement system 22illustrated in FIG. 1); (H) y_(o,YZ2) is the commutation offset of thesecond YZ coil array 242; (iii) k_(y,YZ2) and k_(z,YZ2) are the motorforce constants along Y and Z axis of the second YZ mover 250B (iv)F_(Y2) and F_(Z2) are the motor force commands along the Y and Z axes ofthe second YZ mover 250B, determined by the control system 224, (v)A_(y,YZ2) and A_(z,YZ2) are the required current amplitudes required toproduce the desired force along Y and Z axes respectively for the secondYZ mover 250B and (vi) L is the associated motor commutation pitch.

Further, to control the first XZ mover 250C, the control system 224utilizes the following motor commutations to determine the magnitude ofthe current to be directed to the different phases of the first XZ coilarray 244:

$\begin{matrix}{{\begin{pmatrix}I_{u,{{XZ}\; 1}} \\I_{v,{{XZ}\; 1}} \\I_{w,{{XZ}\; 1}}\end{pmatrix} = {\begin{pmatrix}{\sin \left( {2{\pi \cdot \frac{y + y_{o,{{XZ}\; 1}}}{L}}} \right)} & {\cos \left( {2{\pi \cdot \frac{y + y_{o,{{XZ}\; 1}}}{L}}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{o,{{XZ}\; 1}}}{L}}} + \frac{2\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{y + y_{o,{{XZ}\; 1}}}{L}}} + \frac{2\pi}{3}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{o,{{XZ}\; 1}}}{L}}} + \frac{4\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{y + y_{o,{{XZ}\; 1}}}{L}}} + \frac{4\pi}{3}} \right)}\end{pmatrix} \cdot \begin{pmatrix}A_{y,{{XZ}\; 1}} \\A_{z,{{XZ}\; 1}}\end{pmatrix}}}\mspace{79mu} {A_{y,{{XZ}\; 1}} = \frac{F_{X\; 1}}{k_{y,{{XZ}\; 1}}}}\mspace{79mu} {A_{z,{{XZ}\; 1}} = \frac{F_{Z\; 3}}{k_{z,{{XZ}\; 1}}}}} & {{Equation}\mspace{14mu} (3)}\end{matrix}$

For the first XZ coil array 244, Equation (3) is the motor commutationformula, used to determine the current commands i_(u,XZ1), i_(v,XZ1),and I_(w,XZ1) directed to U, V, W phase coils respectively. Further, inEquation (3), (i) X is the present measured position along the X axis ofthe coil assembly 236 (e.g. as measured with the measurement system 22illustrated in FIG. 1); (ii) x_(o,XZ1) is the commutation offset of thefirst XZ coil array 244; (iii) k_(x,XZ1) and k_(z,XZ1) are theassociated motor force constants along X and Z axis of the first XZmover 250C, (iv) F_(X1) and F_(Z3) are the motor force commands alongthe X and Z axes of the first XZ mover 250C, determined by the controlsystem 224, (v) A_(x,XZ1) and A_(z,XZ1) are the required currentamplitudes required to produce the desired force along X and Z axesrespectively for the first XZ mover 250C and (vi) L is the associatedmotor commutation pitch.

Moreover, to control the second XZ mover 250D, the control system 224utilizes the following motor commutations to determine the magnitude ofthe current to be directed to the different phases of the second XZ coilarray 246:

$\begin{matrix}{{\begin{pmatrix}I_{u,{{XZ}\; 2}} \\I_{v,{{XZ}\; 2}} \\I_{w,{{XZ}\; 2}}\end{pmatrix} = {\begin{pmatrix}{\sin \left( {2{\pi \cdot \frac{x + x_{o,{{XZ}\; 2}}}{L}}} \right)} & {\cos \left( {2{\pi \cdot \frac{x + x_{o,{{XZ}\; 2}}}{L}}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{x + x_{o,{{XZ}\; 2}}}{L}}} + \frac{2\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{x + x_{o,{{XZ}\; 2}}}{L}}} + \frac{2\pi}{3}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{x + x_{o,{{XZ}\; 2}}}{L}}} + \frac{4\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{x + x_{o,{{XZ}\; 2}}}{L}}} + \frac{4\pi}{3}} \right)}\end{pmatrix} \cdot \begin{pmatrix}A_{x,{{XZ}\; 2}} \\A_{z,{{XZ}\; 2}}\end{pmatrix}}}\mspace{79mu} {A_{x,{{XZ}\; 2}} = \frac{F_{Y\; 2}}{k_{y,{{XZ}\; 2}}}}\mspace{79mu} {A_{z,{{XZ}\; 2}} = \frac{F_{Z\; 4}}{k_{z,{{XZ}\; 2}}}}} & {{Equation}\mspace{14mu} (4)}\end{matrix}$

For the second XZ coil array 246, Equation (4) is the motor commutationformula, used to determine the current commands I_(u,XZ2), I_(v,XZ2),and I_(w,XZ2) directed to U, V, W phase coils respectively. Further, inEquation (4), (i) X is the present measured position along the X axis ofthe coil assembly 236 (e.g. as measured with the measurement system 22illustrated in FIG. 1); (ii) x_(o,XZ2) is the commutation offset of thesecond XZ coil array 246; (iii) k_(x,XZ2) and k_(z,XZ2) are theassociated motor force constants along X and Z axis of the second XZmover 250D, (iv) F_(X2) and F_(Z4) are the motor force commands alongthe X and Z axes of the second XZ mover 250D, determined by the controlsystem 224, (v) A_(x,XZ2) and A_(z,XZ2) are the required currentamplitudes required to produce the desired force along X and Z axesrespectively for the second XZ mover 250C and (vi) L is the associatedmotor commutation pitch.

It should be noted that the commutation offset y_(o,YZ1), y_(o,YZ2),x_(o,XZ1), x_(o,XZ2) for each mover 250A-250D is not known. The presentinvention teaches various methods to estimate the commutation offsety_(o,YZ1), y_(o,YZ2), x_(o,XZ1), x_(o,XZ2) for each of the movers250A-250D. In the embodiment illustrated in FIG. 2, the movers 250A-250Dmust be activated to levitate the stage 220A (along the Z axis) duringthe process of determining the commutation offset for each of the movers250A-250D. Moreover, in certain methods provided herein, during theestimation of a selected commutation offset, current is directed to thecorresponding coil array to impart a disturbance on the stage.Subsequently, the forces generated by the mover assembly as a result ofthe disturbance on the stage are evaluated to estimate the commutationoffset.

FIG. 2B is a simplified bottom view of stage 220A and the coil arrays240, 242, 244, 246. As provided above, (i) current directed to the firstYZ coil array 240 generates the first Y axis force 263Y1, and the firstZ axis force 263Z1 (illustrated as a circle); (ii) current directed tothe second YZ coil array 242 generates the second Y axis force 263Y2,and the second Z axis force 263Z2 (illustrated as a circle); (iii)current directed to the first XZ coil array 244 generates the first Xaxis force 263X1, and the third Z axis force 263Z3 (illustrated as acircle); and (iv) current directed to the second XZ coil array 246generates the second X axis force 263X2 that moves the stage 220A alongthe X axis, and the fourth Z axis force 263Z4 (illustrated as a circle).

FIG. 3 is a simplified control block diagram of the control system 224that can be used to control the stage mover assembly 220C (illustratedin FIG. 2) to precisely position the work piece 200 (illustrated in FIG.2). In FIG. 3, (i) “r” represents a desired reference position, e.g. thedesired trajectory (along the X, Y, and Z axes, and about the X, Y, andZ axes) of the work piece 200 at a particular moment in time; (ii) “m”represents the measured, actual momentary, position (along the X, Y, andZ axes, and about the X, Y, and Z axes) of the work piece 200 asmeasured by the measurement system 22 (illustrated in FIG. 1) at aparticular moment in time; and (iii) “e” represents a following error(along the X, Y, and Z axes, and about the X, Y, and Z axes), e.g. theerror between the desired position “r” and the measured output position“m” of the work piece 200 at a particular moment in time.

In FIG. 3, starting at the left side of the control block diagram, thedesired trajectory “r” is fed into the control system 224 along with themeasured position “m”. Next, the control system 224 determines thefollowing error “e”. Subsequently, the following error “e” is fed into afeedback control 352 of the control system 224. The feedback control 352determines the forces along the X, Y and/or Z axes that are necessary tocorrect the following error (e.g. the forces necessary to move a centerof gravity (“CG”) of the stage 220A to the desired trajectory “r”). Incertain embodiments, the one or more of the movers 250A-250D of thestage mover assembly 220C may not push through the center of gravity ofthe stage 220A. In these embodiments, the control system 224 can includea center of gravity force compensation map 354 that compensates forthis.

Next, based on the following error “e”, the force distribution 356determines the force commands for each of the movers 250A-250D necessaryto correct the following error. More specifically, the control systemdetermines the required magnitude of (i) a first Y axis force command(F_(Y1)) and a first Z axis force command (F_(Z1)) for the first YZmover 250A; (ii) a second Y axis force command (F_(Y2)) and a second Zaxis force command (F_(Z2)) for the second YZ mover 250B; (iii) a firstX axis force command (F_(X1)) and a third Z axis force command (F_(Z3))for the first XZ mover 250C; and (iv) a second X axis force command(F_(X2)) and a fourth Z axis force command (F_(Z4)) for the second XZmover 250D. Next, from these force commands, the amplitudes of thecurrents can be determined.

Subsequently, the motor commutations 358 are utilized to determine thecurrents that are directed to the U, V, W phases of the coil arrays 240,242, 244, 246. The currents I_(u,YZ1), U_(v,YZ1), I_(w,YZ1), I_(u,YZ2),I_(v,YZ2), I_(w,YZ2), I_(u,XZ1), I_(v,XZ1), I_(w,XZ1), I_(u,XZ2),I_(v,XZ2), I_(w,XZ2) can be calculated using Equations 1-4. Next, atblock 360, the current is directed to the movers 250A-250D and thiscauses the stage to move.

It should be noted that unless the commutation offsets y_(o,YZ1),y_(o,YZ2), x_(o,XZ1), x_(o,XZ2) for each mover 250A-250D is accuratelyestimated, that the movers 250A-250D will not function as efficientlyand the positioning of the work piece 200 can be adversely influenced.For example, if the commutation offsets y_(o,YZ1), y_(o,YZ2), x_(o,XZ1),x_(o,XZ2) are not correct, the required forces will be larger and theamplitudes of the currents will have to be larger to move the stage tothe desired position.

The present invention provides a number of different ways to accuratelyestimate the commutation offsets y_(o,YZ1), y_(o,YZ2), x_(o,XZ1),x_(o,XZ2). In certain embodiments, the control system 224 includes apossible commutation offset block 361. With this design, during theprocess of estimating the commutation offset of a particular mover,various possible commutation offsets can be used in the respectivecommutation formulas to determine the current for the mover that isbeing evaluated. These processes are described in more detail below.

It should be noted that the methods provided herein can be utilized withmovers in which the coils move relative to stationary magnets or thedesigns in with the magnets move relative to stationary coils.

It should also be noted that the control system 224 can automaticallycalculate the commutation offset for each mover every time the system isstarted or any other time deemed appropriate.

FIG. 4A is a flow chart that illustrates a first process that can beused by the control system 224 to estimate the commutation offsety_(o,YZ1), y_(o,YZ2), x_(o,XZ1), x_(o,XZ2) for each of the movers250A-250D. In this embodiment, at step 470, the stage is levitated usingall of the movers 250A-250D. For example, during step 470, anapproximately correct commutation offset can be used for each of themovers 250A-250D. One way to determine an approximate commutation offsetfor each of the movers 250A-250D is to use a sensor 262 (illustrated asa box in FIG. 2 away from the stage assembly 220) to sense theapproximate relative position between the respective coil array 240,242, 244, 246 and magnet assembly 238. For example, the sensor 262 canbe a hall sensor or another type of sensor. As long as the approximatecommutation offset y_(o,YZ1), y_(o,YZ2), x_(o,XZ1), x_(o,XZ2) isrelatively close to the correct value, the movers 250A-250D should beable to levitate the stage. Alternatively, it can be assumed thateverything is mechanically perfect when the stage assembly is puttogether. This sometimes can be good enough to allow the movers250A-250D to levitate the stage.

Next, the commutation offset y_(o,YZ1), y_(o,YZ2), x_(o,XZ1), x_(o,XZ2)for each of the movers 250A-250D is individually and sequentiallydetermined. More specifically, at step 472, one of the movers 250-250Dis selected for determining its commutation offset. For example, thefirst YZ mover 250A can be initially selected to determine the first YZcommutation offset (“y_(o,YZ1)”). Next, with the stage held in asubstantially constant position (along the X, Y, and Z axes, and aboutthe X, Y, and Z axes) through closed loop control of the movers250A-250D, the control system 224 artificially adjusts the first YZcommutation offset of the first YZ coil array 240 in Equation 1. Statedin another fashion, during this step, the control system 224sequentially utilizes a number of alternative possible commutationoffsets to be used as the first YZ commutation offset in Equation 1.

For each alternative possible commutation offset, at step 476, thecontrol system 224 determines (i) the corresponding Y force command(“F_(Y1)”) for the first YZ mover 250A, and (ii) the corresponding Zforce command (“F_(Z1)”) for the first YZ mover 250A necessary tomaintain the stage in the correct, levitated position. Subsequently, atstep 477, the control system subsequently, determines the amplitude ofthe current (A_(y,XZ1)) required to produce the Y force command(“F_(Y1)”); and the amplitude of the current (A_(z,YZ1)) required toproduce the Z force command (“F_(Z1)”).

As the possible commutation offset changes, the force commands and thecorresponding current commands generated by the control system 224 willchange. This will create a disturbance on the stage. As provided herein,as the possible commutation offset approaches the correct value, the Zforce command F_(Z1) and the corresponding Z axis amplitude of thecurrent (A_(z,ZY1)) for the first YZ mover 250A will decrease; and asthe possible commutation offset moves away from the correct value, the Zforce command F_(Z1) and the corresponding Z axis amplitude of thecurrent (A_(z,YZ1)) for the first YZ mover 250A will increase. Stated inanother fashion, absent external disturbances, the correct possiblecommutation offset occurs at the lowest Z force command F_(Z1) and thelowest Z axis amplitude of the current (A_(z,YZ1)). This is because, asthe possible commutation offset approaches the correct value, the firstYZ mover 250A becomes more efficient and a smaller current is necessaryto maintain the position of the stage. Thus, at step 478, in oneembodiment, the control system 224 determines the correct value for thefirst YZ commutation offset y_(o,YZ1) value by determining the lowest Zforce command F_(Z1) and/or the lowest corresponding Z axis amplitude ofthe current (A_(z,YZ1)) necessary to maintain the position of the stage.

FIG. 4B is a simplified graphic illustration of how the Z force commandcorresponds to various possible commutation offsets y_(o,YZ1). In thisembodiment, the control system 224 identifies the lowest value of Zforce command F_(Z1) on the curve and subsequently identifies itscorresponding possible commutation offset as the first YZ commutationoffset y_(o,YZ1). Alternatively, the control system 224 identifies thelowest value of Z axis amplitude of the current A_(z,YZ1), andsubsequently identifies its corresponding possible commutation offset asthe first YZ commutation offset y_(o,YZ1). In FIG. 4B, the correctcommutation offset is circled with a square.

Referring back to FIG. 4A, after the first YZ commutation offsety_(o,YZ1) is determined, at step 480, the control system 224 determinesif all of the movers 250A-250D have been selected. If not, the nextmover 250A-250D, e.g. the second YZ mover 250B, is selected, and theprocess is repeated to determine the second YZ commutation offset(“y_(o,YZ2)”). Again, with the stage held in a substantially constantposition through closed loop control of the movers 250A-250D, thecontrol system 224 utilizes a plurality of possible commutation offsetsin Equation 2 to direct current to the second YZ coil array 242. Foreach alternative possible commutation offset, the control system 224determines (i) the corresponding Y force command (“F_(Y2)”) and the Yaxis amplitude of the current (A_(y,YZ2)); and (ii) the corresponding Zforce command (“F_(Z2)”) and the Z axis amplitude of the current(A_(z,YZ2)) necessary to maintain the stage in the correct, levitatedposition. The control system 224 determines the correct value for thesecond YZ commutation offset y_(o,YZ2) value by determining the lowest Zforce command F_(Z2) or the lowest Z axis amplitude of the current(A_(z,YZ2)) necessary to maintain the position of the stage.

This process is again repeated for the first XZ mover 250C to determinethe first XZ commutation offset (“x_(o,XZ1)”). Again, with the stageheld in a substantially constant position through closed loop control ofthe movers 250A-250D, the control system 224 utilizes a plurality ofpossible commutation offsets in Equations 3 to direct current to thefirst XZ coil array 244. For each alternative possible commutationoffset, the control system 224 determines (i) the corresponding X forcecommand (“F_(X1)”) and the X axis amplitude of the current (A_(x,XZ1));and (ii) the corresponding Z force command (“F_(Z3)”) and the Z axisamplitude of the current (“A_(z,XZ1)”) necessary to maintain the stagein the correct, levitated position. The control system 224 determinesthe correct value for the first XZ commutation offset x_(o,XZ1) value bydetermining the lowest Z force command F_(Z3) or the lowest Z axisamplitude of the current (“A_(z,XZ1)”) necessary to maintain theposition of the stage.

Finally, the process is repeated for the second XZ mover 250D todetermine the second XZ commutation offset (“x_(o,XZ2)”). Again, withthe stage held in a substantially constant position through closed loopcontrol of the movers 250A-250D, the control system 224 utilizes aplurality of possible commutation offsets in Equations 4 to directcurrent to the second XZ coil array 246. For each alternative second XZcommutation offset, the control system 224 determines (i) thecorresponding X force command (“F_(X2)”) and the X axis amplitude of thecurrent (A_(z,XZ2)); and (ii) the corresponding Z force command(“F_(Z4)”) and the Z axis amplitude of the current (Z_(z,XZ2)) necessaryto maintain the stage in the correct, levitated position. The controlsystem 224 determines the correct value for the second XZ commutationoffset x_(o,XZ2) value by determining the lowest Z force command F_(z4)or the lowest Z axis amplitude of the current (A_(z,XZ2)) necessary tomaintain the position of the stage.

After all of the movers 250A-250D have been selected, this commutationprocess is completed at step 482. It should be noted that one advantageof this method is that it relies on adjusting only the Z force. As aresult thereof, any disturbance forces along X and Y axes should notadversely influence the calculations of the commutation offsets. Itshould also be noted that the sequence of determining the commutationoffsets for the movers 250A-250D can be different than that describedherein.

In summary, with this embodiment, a constant Z force is required fromeach of the movers 250A-250D to support the weight of the stage. Next,the commutation offset for one mover 250A-250D at a time can be smoothlyadjusted. As the possible offset changes, the required commutationamplitude to provide the necessary Z force will change. As the possibleoffset approaches the correct value, the Z commutation amplitude willdecrease, although the actual Z force remains constant. In this way, thesoftware of the control system 224 can search for the commutation offsetwhere the constant Z force is produced with the minimum commutationamplitude. This value should be the correct commutation offset to usefor that mover.

FIG. 5A is a flow chart that illustrates a different process that can beused by the control system 224 to estimate the commutation offsety_(o,YZ1), y_(o,YZ2), x_(o,XZ1), x_(o,XZ2) for each of the movers250A-250D. In this embodiment, at step 570, the stage is levitated usingall of the movers 250A-250D. For example, during step 570, anapproximately correct commutation offset can be used for each of themovers 250A-250D.

Next, the commutation offset y_(o,YZ1), y_(o,YZ2), x_(o,XZ1), x_(o,XZ2)for each of the movers 250A-250D is individually and sequentiallydetermined. More specifically, at step 572, one of the movers 250-250Dis selected for determining its commutation offset. For example, thefirst YZ mover 250A can be initially selected to determine the first YZcommutation offset (“y_(o,YZ1)”). Next, at step 574, with the stage heldin a substantially constant position through closed loop control of themovers 250A-250D, the control system 224 sequentially selects a numberof alternative possible commutation offsets for use in Equation 1.

For each alternative possible commutation offset, at step 576, thecontrol system 224 determines (i) the corresponding Y force command(“F_(Y1)”) for the first YZ mover 250A, and (ii) the corresponding Zforce command (“F_(Z1)”) for the first YZ mover 250A necessary tomaintain the stage in the correct position along the Y axis.Subsequently, at step 577, the control system subsequently, determinesthe Y axis amplitude of the current (A_(y,YZ1)) required to produce theY force command (“F_(Y1)”); and the Z axis amplitude of the current(A_(z,YZ1)) required to produce the Z force command (“F_(Z1)”).

As the possible commutation offset changes, the force commands and thecorresponding current commands generated by the control system 224 willchange. More specifically, absence disturbances, as the possiblecommutation offset approaches the correct value, the Y force commandF_(Y1) and the corresponding Y axis amplitude of the current (A_(y,YZ1))for the first YZ mover 250A will approach zero; and as the possiblecommutation offset moves away from the correct value, the Y forcecommand F_(Y1) and the corresponding Y axis amplitude of the current(A_(y,YZ1)) for the first YZ mover 250A will move away from zero. Statedin another fashion, absent disturbances, the correct possiblecommutation offset occurs at a zero Y force command F_(Y1) and a zero Yaxis amplitude of the current (A_(y,YZ1)). This is because, absentdisturbances, zero force is required to maintain the position of thestage along the Y axis. Thus, at step 578, in one embodiment, thecontrol system 224 determines the correct value for the first YZcommutation offset y_(o,YZ1) value by determining when the Y forcecommand F_(Y1) and/or the corresponding Y axis amplitude of the current(A_(Y1)) is zero.

FIG. 5B is a graphic illustration of how the Y force command correspondsto various first YZ commutation offsets y_(o,YZ1). In this embodiment,the control system 224 identifies when the Y force command F_(Y1) isequal to zero, and subsequently identifies its corresponding possiblecommutation offset as the first YZ commutation offset y_(o,YZ1). In FIG.5B, the correct commutation offset is circled with a square. Oneadvantage of this method is that the Y force command F_(Y1) versus YZcommutation offset y_(o,YZ1) curve crosses zero and has a maximum slopeat zero (the correct YZ commutation offset y_(o,YZ1). This makes iteasier to determine the proper YZ commutation offset y_(o,YZ1).

Referring back to FIG. 5A, after the first YZ commutation offsety_(o,YZ1) is determined, at step 578, the control system 224 determinesif all of the movers 250A-250D have been selected. If not, the nextmover 250A-250D, e.g. the second YZ mover 250B, is selected, and theprocess is repeated to determine the second YZ commutation offset(“y_(o,YZ2)”). Again, with the stage held in a substantially constantposition through closed loop control of the movers 250A-250D, thecontrol system 224 utilizes a plurality of possible commutation offsetsin Equation 2 to direct current to the second YZ coil array 242. Foreach alternative possible commutation offset, the control system 224determines (i) the corresponding Y force command (“F_(Y2)”) and Y axisamplitude of the current (A_(y,YZ2)); and (ii) the corresponding Z forcecommand (“F_(Z2)”) and the Z axis amplitude of the current (A_(z,YZ2))necessary to maintain the stage in the correct position. The controlsystem 224 determines the correct value for the second YZ commutationoffset y_(o,YZ2) value by determining when the Y force command F_(Y2)and/or the corresponding Y axis amplitude of the current (A_(y,YZ2)) iszero or approximately zero.

This process is again repeated for the first XZ mover 250C to determinethe second XZ commutation offset (“x_(o,XZ1)”). Again, with the stageheld in a substantially constant position through closed loop control ofthe movers 250A-250D, the control system 224 utilizes a plurality ofpossible commutation offsets in Equation 3 to direct current to thefirst XZ coil array 244. For each alternative possible commutationoffset, the control system 224 determines (i) the corresponding X forcecommand (“F_(X1)”) and the X axis amplitude of the current (A_(x,XZ1));and (ii) the corresponding Z force command (“F_(Z3)”) and the Z axisamplitude of the current (A_(z,XZ1)) necessary to maintain the stage inthe correct position. The control system 224 determines the correctvalue for the first XZ commutation offset x_(o,XZ1) value by determiningwhen the X force command F_(X1) and/or the corresponding X axisamplitude of the current (A_(x,XZ1)) is zero.

Finally, the process is repeated for the second XZ mover 250D todetermine the second XZ commutation offset (“x_(o,XZ2)”). Again, withthe stage held in a substantially constant position through closed loopcontrol of the movers 250A-250D, the control system 224 utilizes aplurality of possible commutation offsets in Equation 4 to directcurrent to the second XZ coil array 246. For each alternative possiblecommutation offset, the control system 224 determines (i) thecorresponding X force command (“F_(X2)”) and the X axis amplitude of thecurrent (A_(x,XZ2)); and (ii) the corresponding Z force command(“F_(Z4)”) and the Z axis amplitude of the current (A_(z,XZ2)) necessaryto maintain the stage in the correct position. The control system 224determines the correct value for the second XZ commutation offsetX_(o,XZ2) value by determining when the X force command F_(X2) and/orthe corresponding X axis amplitude of the current (A_(x,XZ2)) is zero orapproximately zero.

After all of the movers 250A-250D have been selected, this commutationprocess is completed at step 582.

FIG. 6 is a simplified control block diagram of another embodiment of acontrol system 624 that can be used to determine the commutation offsetfor each of the movers 250A-250D (illustrated in FIG. 2). In thisembodiment, the control block diagram 624 is somewhat similar to thecontrol block diagram illustrated in FIG. 3. However, in FIG. 6, thecontrol system 624 includes three test related blocks, namely a testforce command block 670, a test commutation block 672, and an actualforce output block 674.

It should be noted that the test related blocks 670, 672, 674 are usedto evaluate only one mover 250A-250D at a time, and only during thedetermination of its commutation offset. Stated in another fashion,during the calibration of each mover, the test related blocks 670, 672,674 are used with the closed loop control the mover 250A-250D beingevaluated, and the test related blocks 670, 672, 674 are not used tocontrol the movers 250A-250D that are not currently being evaluated.Subsequently, after all of the movers 250A-250D have been evaluated, thecontrol block diagram 624 without the test related blocks 670, 672, 674can be used to control the movers 250A-250D during usage of the stageassembly.

In FIG. 6 (similar to FIG. 3), (i) “r” represents a desired referenceposition; (ii) “m” represents the measured, actual momentary, position;and (iii) “e” represents a following error between the desired position“r” and the measured output position “m”. Further, starting at the leftside of the control block diagram 624, the desired trajectory “r” is fedinto the control system 624 along with the measured position “m”. Next,the control system 624 determines the following error “e”. Subsequently,the following error “e” is fed into a feedback control 652 of thecontrol system 624. The feedback control 652 determines the forces alongthe X, Y and/or Z axes that are necessary to correct the following error(e.g. the forces necessary to move a center of gravity (“CG”) of thestage 220A to the desired trajectory “r”). One or more of the movers250A-250D of the stage mover assembly 220C may not push through thecenter of gravity of the stage 220A. In these embodiments, the controlsystem 624 can include a center of gravity force compensation map 654that compensates for this.

Next, a force distribution 656 determines the force commands for each ofthe movers 250A-250D necessary to correct the following error. Based onthe following error “e”, the control system 224 determines the magnitudeof the forces generated by the movers 250A-250D necessary to correct thefollowing error. More specifically, the control system determines therequired magnitude of (i) a first Y force command (F_(Y1)) and a first Zforce command (F_(Z1)) for the first YZ mover 250A; (ii) a second Yforce command (F_(Y2)) and a second Z force command (F_(Z2)) for thesecond YZ mover 250B; (iii) a first X force command (F_(X1)) and a thirdZ force command (F_(Z3)) for the first XZ mover 250C; and (iv) a secondX force command (F_(X2)) and a fourth Z force command (F_(Z4)) for thesecond XZ mover 250D. Subsequently, from these force commands, theamplitudes of the currents can be determined. More specifically, (i)A_(y,YZ1) can be determined from the first Y force command F_(Y1); (ii)A_(z,YZ1) can be determined from the first Z force command F_(Z1); (iii)A_(y,YZ2) can be determined from the second Y force command F_(Y2); (iv)A_(z,YZ2) can be determined from the second Z force command F_(Z2); (v)A_(z,XZ1) can be determined from the first X force command F_(x1); (vi)A_(z,XZ1) can be determined from the third Z force command F_(z3); (vii)A_(x,XZ2) can be determined from the second X force command F_(X2); and(viii) A_(z,XZ2) can be determined from the fourth Z force commandF_(Z4).

With the present invention, the control system 624 imparts a test forcecommand 670 on the selected mover 250A-250D at block 670. The magnitudeof the test force can be varied pursuant to the teachings providedherein. The test force command should be large enough to have a goodsignal to noise ratio, but small enough not to make the closed loopcontrol of the position of the stage unstable. In one non-exclusiveembodiment, the test force command can be sixty Newton. Alternatively,the test force command can be greater or less than sixty Newton

To maintain the same closed-loop system behaviors during calibration, anextra motor commutation function may be conducted to transform the testforce command to test current commands for the mover 250A-250D that isbeing calibrated. Those test current commands then are added up to thosein the closed loop before being sending out to the amplifiers. Morespecifically, the test commutation 672 and the mover commutations 658are utilized to determine the currents that are directed to the U, V, Wphases of the particular coil array 240, 242, 244, 246 being calibrated.Further, the mover commutations 658 (without the test commutation 672)are utilized to determine the currents that are directed to the U, V, Wphases of the other coil arrays 240, 242, 244, 246 that are notcurrently being tested. Thus, during calibration, for the three movers250A-250D that are not currently being tested, the U, V, W currents canbe calculated using Equations 1-4.

If the mover 250A-250D being tested is a YZ mover 250A, 250B, thefollowing commutation equations can be used to determine the magnitudeof the current to be directed to the different phases of that YZ mover250A, 250B:

$\begin{matrix}{\begin{pmatrix}I_{{u,{YZ}}\;} \\I_{{v,{YZ}}\;} \\I_{{w,{YZ}}\;}\end{pmatrix} = {{\begin{pmatrix}{\sin \left( {2{\pi \cdot \frac{y + y_{{o,{YZ}}\;}}{L}}} \right)} & {\cos \left( {2{\pi \cdot \frac{y + y_{{o,{YZ}}\;}}{L}}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{{o,{YZ}}\;}}{L}}} + \frac{2\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{y + y_{{o,{YZ}}\;}}{L}}} + \frac{2\pi}{3}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{{o,{YZ}}\;}}{L}}} + \frac{4\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{y + y_{{o,{YZ}}\;}}{L}}} + \frac{4\pi}{3}} \right)}\end{pmatrix} \cdot \begin{pmatrix}A_{{y,{YZ}}\;} \\A_{{z,{YZ}}\;}\end{pmatrix}} + {\begin{pmatrix}{\sin \left( {2{\pi \cdot \frac{y + y_{{o,{TE}}\;}}{L}}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{{o,{TE}}\;}}{L}}} + \frac{2\pi}{3}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{y + y_{{o,{TE}}\;}}{L}}} + \frac{4\pi}{3}} \right)}\end{pmatrix} \cdot {A_{T}.}}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

In this Equation, (i) I_(u,YZ) is the current directed to the U phasecoil(s); (ii) I_(v,YZ) is the current directed to the V phase coil(s);(iii) I_(w,YZ) is the current directed to the W phase coil(s); (iv) y isthe present measured position along the Y axis; (v) A_(y,YZ) is theamplitude of the current (“Y axis current amplitude”) required toproduce the desired force along the Y axis for the selected YZ mover250A/B determined by the control system 224; (vi) A_(z,YZ) is theamplitude of the current (“Z axis current amplitude”) required toproduce the desired force along the Z axis for the selected YZ mover250A/B determined by the control system 224; (vii) A_(T) is theamplitude of the current (“Test current amplitude”) required to producethe desired test force along the Y axis for the selected YZ mover 250A/Bdetermined by the control system 224; (vii) y_(o,YZ) is the defaultoffset, roughly determined beforehand and (viii) y_(o,TE) is a possibletest offset.

It should be noted that these equations combine both the testcommutation 672 and the mover commutations 658 into the same equation.Further, during the process of estimating the commutation offset of aparticular YZ mover 250A, 250B, various possible test offsets aresequentially used in Equation (5) to determine the current for the moverthat is being evaluated.

Somewhat similarly, if the mover being tested is a XZ mover 250C, 250D,the following commutation equations can be used to determine themagnitude of the current to be directed to the different phases of thatXZ mover:

$\begin{matrix}{\begin{pmatrix}I_{{u,{YZ}}\;} \\I_{{v,{YZ}}\;} \\I_{{w,{YZ}}\;}\end{pmatrix} = {{\begin{pmatrix}{\sin \left( {2{\pi \cdot \frac{x + x_{{o,{XZ}}\;}}{L}}} \right)} & {\cos \left( {2{\pi \cdot \frac{x + x_{{o,{XZ}}\;}}{L}}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{x + x_{{o,{XZ}}\;}}{L}}} + \frac{2\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{x + x_{{o,{XZ}}\;}}{L}}} + \frac{2\pi}{3}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{x + x_{{o,{XZ}}\;}}{L}}} + \frac{4\pi}{3}} \right)} & {\cos \left( {{2{\pi \cdot \frac{x + x_{{o,{XZ}}\;}}{L}}} + \frac{4\pi}{3}} \right)}\end{pmatrix} \cdot \begin{pmatrix}A_{{x,{XZ}}\;} \\A_{{z,{XZ}}\;}\end{pmatrix}} + {\begin{pmatrix}{\sin \left( {2{\pi \cdot \frac{x + x_{{o,{TE}}\;}}{L}}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{x + x_{{o,{TE}}\;}}{L}}} + \frac{2\pi}{3}} \right)} \\{\sin \left( {{2{\pi \cdot \frac{x + x_{{o,{TE}}\;}}{L}}} + \frac{4\pi}{3}} \right)}\end{pmatrix} \cdot A_{T}}}} & {{Equation}\mspace{14mu} (6)}\end{matrix}$

In Equation 6, (i) I_(u,XZ) is the current directed to the U phasecoil(s); (ii) I_(v,XZ) is the current directed to the V phase coil(s);(iii) I_(w,XZ) is the current directed to the W phase coil(s); (iv) X isthe present measured position along the X axis; (v) A_(x,XZ) is theamplitude of the current (“X axis current amplitude”) required toproduce the desired force along the X axis for the selected XZ mover250C, 250D determined by the control system 224; (vi) A_(z,XZ) is theamplitude of the current (“Z axis current amplitude”) required toproduce the desired force along the Z axis for the selected XZ mover250C, 250D determined by the control system 224; (vii) A_(T) is theamplitude of the current (“Test current amplitude”) required to producethe desired test force along the X axis for the selected XZ mover 250C,250D determined by the control system 224; (vii) x_(o,YZ) is the defaultoffset, roughly determined beforehand, and (viii) x_(o,TE) is a possibletest offset.

Next, at block 660, the current is directed to the movers 250A-250D andthis causes the stage to move. It should be noted that the force outputblock 674 is used to determine the actual force along the X, Y and Zaxis that results from the test force being imparted by the mover beingtested. Stated in another fashion, when the test force is imparted bythe mover being evaluated, the control system 624 operating in a closedloop fashion, must determine the other forces necessary to maintain theposition of the stage. Thus, the force output block 674 is used toprovide the actual force imparted on the stage by the test forcecommand.

As provided herein, if one of the YZ movers is being tested, and if thetest offset is close to optimal, a test force command of sixty Newtonalong the Y axis will impart an actual force on the stage of (i)approximately sixty Newton and reaching its maximal magnitude along theY axis, (ii) approximately zero Newton along the Z axis, and (iii)approximately zero Newton along the X axis. However, when the testoffset is not correct, a test force command of sixty Newton along the Yaxis will result in an actual force on the stage of (i) less than sixtyNewton along the Y axis, (ii) non-zero Newton along the Z axis, and(iii) non-zero Newton along the X axis. Similarly, if one of the XZmovers is being tested, and if the test offset is close to optimal, atest force command of sixty Newton along the X axis will impart anactual force on the stage of (i) approximately sixty Newton and reachingits maximal magnitude along the X axis, (ii) approximately zero Newtonalong the Z axis, and (iii) approximately zero Newton along the Y axis.However, when the test offset is not correct, a test force command ofsixty Newton along the X axis will result in an actual force on thestage of (i) less than sixty Newton along the X axis, (ii) non-zeroNewton along the Z axis, and (iii) non-zero along the Y axis.

It should be noted that, in order to measure the resulting forcegenerated by the test force command 670, the original stagecenter-of-gravity force command values before calibration with a zerotest force command 675 needs to be subtracted from those duringcalibration prior to the force output block 674.

FIG. 7 is a flow chart that illustrates a process that can be used bythe control system 624 to sequentially estimate the commutation offsety_(o,YZ1), y_(o,YZ2), x_(o,XZ1), x_(o,XZ2) for each of the movers250A-250D. In this embodiment, at step 770, the stage is levitated usingall of the movers 250A-250D. For example, during step 770, anapproximately correct commutation offset can be used for each of themovers 250A-250D.

Next, the commutation offset y_(o,YZ1), y_(o,YZ2), x_(o,XZ1), x_(o,XZ2)for each of the movers 250A-250D is individually and sequentiallydetermined while the stage is maintained in a levitated position usingclosed loop control. More specifically, at step 772, one of the movers250-250D is selected for determining its commutation offset. Forexample, the first XZ mover 250C can be initially selected to determinethe first XZ commutation offset (“x_(o,XZ1)”). Next, with the stage heldin a substantially constant position through closed loop control of themovers 250A-250D, the control system 224 applies a test force along theX axis, e.g. sixty Newton to the command of the first XZ mover 250C.FIG. 8A is graph that illustrates a test force (entered into the testforce command 670 of FIG. 6) versus time. In this example, the testforce command of sixty Newton along the X axis is applied from time zeroto time seventy-two seconds by the first XZ mover 250C.

At this time, current to the U, V, W, phases of the first XZ mover 250Care determined. At step 776, the possible test offsets are sequentiallyvaried. FIG. 8B is graph that illustrates possible test offsets versustime. In this example, the possible test offset varies from zero toseventy-two millimeters from time zero to time seventy-two seconds. Inthis example, the test offset for the test force command is graduallychanged from the default value to cover the entire commutation pitch (72mm). The test offset will then generate extra three phase currentcommands for the mover that is being calibrated. These extra three phasecurrent commands versus time are illustrate in FIG. 8C.

At step 778, the control system calculates the force commands and thecorresponding current amplitudes for each test offset for the selectedmover. Stated in another fashion, in the present example, for eachpossible test offset, current to the U, V, W, phases of the first XZmover 250C are determined, and the forces are applied to the stage. FIG.8C is graph that illustrates the resulting open current commandsdirected to the U phase (illustrated with a solid line), the V phase(illustrated with a long dashed line), and the W phase (illustrated witha short dashed line) for the first XZ mover 250C versus time. Basically,FIG. 8C illustrates how the current to the U, V, W phases of the firstXZ mover 250C varies with a constant test force, and a changing testoffset.

Next, at step 780, the actual force output from the test force commandfor each test offset is determined by the force output 674 (illustratedin FIG. 6). FIG. 8D is a graph that illustrates the X axis forceimparted on the stage as a result of the test force for each testoffset; FIG. 8E is a graph that illustrates the Z axis force imparted onthe stage as a result of the test force for each test offset; and FIG.8F is a graph that illustrates the Y axis force imparted on the stage asa result of the test force for each test offset. It should be noted thatfor the XZ mover, the X force and the Z force vary greatly as the testoffset varies, while the Y force varies only slightly as the test offsetvaries.

Referring back to FIG. 7, at step 782, using the data regarding theactual force output, the control system determines the first XZcommutation offset for the first XZ mover 250C.

The actual procedure used to determine the first XZ commutation offsetfrom this data can be varied. As one non-exclusive example, the controlsystem 624 can utilize the X axis force data (illustrated in FIG. 8D) todetermine the first XZ commutation offset. In this example, the first XZmover 250C was designed and assembled so that the first XZ coil array244 is properly aligned at the X position of thirty-six millimeters.However, referring to FIG. 8D, the X force data has the largest negativevalue at a test offset of approximately 35.35 millimeters. In thisexample, the first XZ commutation offset can be determined by theabsolute value of the X designed position minus the test offset. In thissimplified example, the first XZ commutation offset is 0.65(|36−35.35|=0.65).

In an alternative embodiment, the control system 624 can utilize the Zaxis force data (illustrated in FIG. 8E) to determine the first XZcommutation offset. In this example, the first XZ mover 250C wasdesigned and assembled so that the first XZ coil array 244 is properlyaligned at the Z position of eighteen millimeters. However, referring toFIG. 8E, the Z axis force data has the largest negative value at a testoffset of approximately 17.42 millimeters. In this example, the first XZcommutation offset can be determined by the absolute value of the Zdesigned position minus the test offset. In this simplified example, thefirst XZ commutation offset is 0.58 (|18−17.42|=0.58).

In yet another embodiment, the first XZ commutation offset can be theaverage value of that determined utilizing the X axis force data and theZ axis force data. In the example provided herein, the first XZcommutation offset would be equal to 0.615 ((0.65+0.58)/2=0.615).

Referring back to FIG. 7, in still another embodiment, for each selectedmover, at optional step 781 (illustrated with a dashed box), thepreviously described steps 774-780 can be repeated for a number ofalternative positions for the stage relative to the stage base. Thenumber of alternative positions can be varied. For example, with aconstant Z position of the stage, steps 774-780 can be repeated for afirst X-Y stage position, a second X-Y stage position, a third X-Y stageposition, and a fourth X-Y stage position. In this example, stage ismoved along the X axis and/or the Y axis between the different X-Y stagepositions.

FIG. 8G is a graph that illustrates the X axis force imparted on thestage as a result of the test force for a portion of the test offsetsand for each X-Y stage position; and FIG. 8H is a graph that illustratesthe Z axis force imparted on the stage as a result of the test force fora portion of the test offsets and for each X-Y stage position. It shouldbe noted that in FIGS. 8G and 8H, (i) line 801 (short dashes) representsthe results for the first X-Y stage position, (ii) line 803 (solid line)represents the results for the second X-Y stage position, (iii) line 805(long dashes) represents the results for the third X-Y stage position,and (iv) line 807 (dotted line) represents the results for the fourthX-Y stage position. Further, for clarity, (i) in FIG. 8G, the testoffsets are only illustrated near the designed position of 36millimeters; and (ii) in FIG. 8H, the test offsets are only illustratednear the designed position of 18 millimeters.

In this example, the first XZ commutation offset can be determined fromthe absolute value of the X designed position minus the average value ofthe test offset for each X-Y stage position using the X axis forces.Referring to FIG. 8G, in this simplified example, (i) for the first X-Ystage position, the test offset is 35.9; (ii) for the second X-Y stageposition, the test offset is 35.8; (iii) for the third X-Y stageposition, the test offset is 35.7; and (iv) for the fourth X-Y stageposition, the test offset is 36.2. In this embodiment, the first XZcommutation offset is 0.1 (|36−((35.9+35.8+35.7+36.2)/4)|=0.1).

Alternatively, in this example, the first XZ commutation offset can bedetermined the absolute value of the Z designed position minus theaverage value of the test offset for each X-Y stage position using the Zaxis forces. Referring to FIG. 8H, in this simplified example, (i) forthe first X-Y stage position, the test offset is 17.7; (ii) for thesecond X-Y stage position, the test offset is 17.8; (iii) for the thirdX-Y stage position, the test offset is 17.9; and (iv) for the fourth X-Ystage position, the test offset is 17.6. In this embodiment, the firstXZ commutation offset is 0.25 (|18−((17.7+17.8+17.9+17.6)/4)|=0.25).

In yet another embodiment, the first XZ commutation offset can be theaverage value of that determined utilizing the X axis force data and theZ axis force data for the plurality of X-Y positions. In this example,first XZ commutation offset is 0.175 ((0.1+0.25)/2=0.175).

In still another alternative embodiment, the stage can be maintained ata substantially constant X-Y position and the Z axis position of thestage can be changed. For example, with a constant X-Y position of thestage, steps 774-780 can be repeated for a first Z stage position, asecond Z stage position, a third Z stage position, and a fourth Z stageposition. FIG. 81 is a graph that illustrates the X axis force impartedon the stage as a result of the test force for a portion of the testoffsets and for each Z stage position; and FIG. 8J is a graph thatillustrates the Z axis force imparted on the stage as a result of thetest force for a portion of the test offsets and for each Z stageposition. It should be noted that in FIGS. 8I and 8J, (i) line 809(short dashes) represents the results for the first Z stage position,(ii) line 811 (solid line) represents the results for the second Z stageposition, (iii) line 813 (long dashes) represents the results for thethird Z stage position, and (iv) line 815 (dotted line) represents theresults for the fourth Z stage position. Further, for clarity, (i) inFIG. 81, the test offsets are only illustrated near the designed X axisposition of 36 millimeters; and (ii) in FIG. 8J, the test offsets areonly illustrated near the designed Z axis position of 18 millimeters.

In this example, the first XZ commutation offset can be determined fromthe absolute value of the X designed position minus the average value ofthe test offset for each Z stage position using the X axis force.Referring to FIG. 81, in this simplified example, (i) for the first Zstage position, the test offset is 36.5; (ii) for the second Z stageposition, the test offset is 35.5; (iii) for the third Z stage position,the test offset is 35.0; and (iv) for the fourth Z stage position, thetest offset is 35.7. In this embodiment, the first XZ commutation offsetis 0.325 (|36−((36.5+35.5+35.0+35.7)/4)|=0.325).

Alternatively, in this example, the first XZ commutation offset can bedetermined the absolute value of the Z designed position minus theaverage value of the test offset for each Z stage position using the Zaxis force. Referring to FIG. 8H, in this simplified example, (i) forthe first Z stage position, the test offset is 17.0; (ii) for the secondZ stage position, the test offset is 17.5; (iii) for the third Z stageposition, the test offset is 17.7; and (iv) for the fourth Z stageposition, the test offset is 18.5. In this embodiment, the first XZcommutation offset is 0.675 (|18−((17.0+17.5+17.7+18.5)/4)|=0.675).

In yet another embodiment, the first XZ commutation offset can be theaverage value of that determined utilizing the X axis force data and theZ axis force data for the plurality of Z positions. In this example,first XZ commutation offset is 0.5 ((0.325+0.675)/2=0.5).

Referring back to FIG. 7, after the first XZ commutation offsetx_(o,XZ1) is determined, at step 784, the control system 624 determinesif all of the movers 250A-250D have been selected. If not, at step 772,the next mover 250A-250D, e.g. the second XZ mover 250D, can beselected, and the process is repeated to determine the second XZcommutation offset (“x_(o,XZ2)”). Again, with the stage held in asubstantially constant position through closed loop control of themovers 250A-250D, the control system 224 applies the test force and atstep 776, the possible test offsets are sequentially varied.

At step 778, the control system calculates the force commands and thecorresponding current amplitudes for each test offset for the selectedmover. Stated in another fashion, in the present example, for eachpossible test offset, current to the U, V, W, phases of the second XZmover 250D are determined, and the forces are applied to the stage.

Next, at step 780, the actual force output from the test force for eachtest offset is determined by the force output 674 (illustrated in FIG.6). At step 782, using the data regarding the force output, the controlsystem determines the second XZ commutation offset for the second XZmover 250D. The procedures described above can be used to determine thesecond XZ commutation offset from this data.

As one non-exclusive example, the control system 624 can utilize the Xforce data, the Z force data or a combination thereof to calculate thesecond XZ commutation offset.

After the second XZ commutation offset x_(o,XZ2) is determined, at step784, the control system 624 determines if all of the movers 250A-250Dhave been selected. If not, at step 772, the next mover 250A-250D, e.g.the first YZ mover 250A, can be selected, and the process is repeated todetermine the first YZ commutation offset (“y_(o,YZ1)”). Again, with thestage held in a substantially constant position through closed loopcontrol of the movers 250A-250D, the control system 224 applies the Ytest force and at step 776, the possible test offsets are sequentiallyvaried.

At step 778, the control system calculates the force commands and thecorresponding current amplitudes for each test offset for the selectedmover. Stated in another fashion, in the present example, for eachpossible test offset, current to the U, V, W, phases of the first YZmover 250A are determined, and the forces are applied to the stage.

Next, at step 780, the actual force output from the test force for eachtest offset is determined by the force output 674 (illustrated in FIG.6). It should be noted that for the YZ mover, the Y force and the Zforce vary greatly as the test offset varies, while the X force variesonly slightly as the test offset varies. At step 782, using the dataregarding the force output, the control system determines the first YZcommutation offset for the first YZ mover 250A. Somewhat similarprocedures as described above can be used to determine the first YZcommutation offset from this data.

As non-exclusive examples, the control system 624 can utilize the Y axisforce data, the Z axis force data or a combination thereof (with orwithout various X-Y-Z positions) to calculate the first YZ commutationoffset.

After the first YZ commutation offset y_(o,YZ1) is determined, at step784, the control system 624 determines if all of the movers 250A-250Dhave been selected. If not, at step 772, the next mover 250A-250D, e.g.the second YZ mover 250A, can be selected, and the process is repeatedto determine the second YZ commutation offset (“y_(o,YZ2)”). Again, withthe stage held in a substantially constant position through closed loopcontrol of the movers 250A-250D, the control system 224 applies the Ytest force and at step 776, the possible test offsets are sequentiallyvaried.

At step 778, the control system calculates the force commands and thecorresponding current amplitudes for each test offset for the selectedmover. Stated in another fashion, in the present example, for eachpossible test offset, current to the U, V, W, phases of the second YZmover 250B are determined, and the forces are applied to the stage.

Next, at step 780, the actual force output from the test force for eachtest offset is determined by the force output 674 (illustrated in FIG.6). At step 782, using the data regarding the force output, the controlsystem determines the second YZ commutation offset for the second YZmover 250B. Somewhat similar procedures as described above can be usedto determine the second YZ commutation offset from this data. Asnon-exclusive examples, the control system 624 can utilize the Y axisforce data, the Z axis force data or a combination thereof (with orwithout various X-Y-Z positions) to calculate the second YZ commutationoffset.

After all of the movers 250A-250D have been selected, this commutationprocess is completed at step 786. It should be noted that with thisprocedure, because all the closed-loop parameters, including feedbackfilter parameters, force distribution matrix, and motor commutationsremain the same during the entire calibration process, the systemstability and closed-loop performance maintain its good shape withoutany concern. Furthermore, because the force output is associated withthe test force command, any cable force effect can be completely removedfrom the calibration.

The present invention is also directed to one or more compensationmethods that significantly reduce the following error for the stageassemblies 18, 20 (illustrated in FIG. 1). For example, the compensationmethods disclosed herein can be used to reduce the following error for aplanar motor type stage assembly 220 like that illustrated in FIG. 2A.Alternatively, the compensation methods disclosed herein can be used toreduce the following error for all different types of movers, such as asingle axis linear mover, a two axis mover, or a three axis mover.Moreover, the compensation methods disclosed herein can be used in moverdesigns that utilize coils that are moved relative to magnets, ormagnets that are moved relative to coils.

As provided herein, in one embodiment, the compensation method is usedby the control system 24 (illustrated in FIG. 1) to generate a separatecompensation map for each stage mover assembly 18C, 20C that details thespecific characteristics of each stage mover assembly 18C, 20C overtheir entire range of travel or a portion thereof. Subsequently, thecompensation maps are used by the control system 24 to control therespective stage mover assembly 18C, 20C, and position each stage 18A,20A (illustrated in FIG. 1) with improved accuracy.

Referring back to FIG. 2A, in one embodiment, the stage mover assembly220C includes four sets of three-phase, two degree of freedom movers250A, 250B, 250C, 250D. Further, each of the movers 250A, 250B, 250C,250D generates either an X or Y force, and a Z force. In thisembodiment, the control system 224 utilizes eight mover force commands(two for each mover) to control the four movers 250A, 250B, 250C, 250Dto position the stage 220A with six degrees of freedom (along the X, Y,and Z axes, and about the X, Y, and Z axes). With this design, there aretwo redundant Z forces created by the movers 250A, 250B, 250C, 250D thatcan be used to minimize twisting force and to balance theta Z momentcontribution from the X and Y forces. Further, the pitch moments due tothe X and Y forces can be cancelled by the mover Z force commands.

FIG. 9 is a simplified graph that illustrates the steps that can beperformed by the processor of the control system to generate thecompensation map. As an overview, in one embodiment, the control systemuses one or more, single frequency excitation signals at a plurality ofalternative, stage test positions to check force ripples and side forceeffects on the center of gravity force/moment commands for the moverassembly at each of the test positions. Subsequently, the control systemcan generate the compensation map from the information of theforce/moment commands.

As provided herein, at step 900, a plurality of alternative testpositions are determined. The number of alternative test positions canbe varied. Generally speaking, the accuracy of the positioning of thestage increases as the number of alternative test positions isincreased. For example, FIG. 10A is a simplified illustration of onenon-exclusive example of a plurality of alternative test positions 1010,with each test position 1010 being represented as a small circle. Inthis example, there are two hundred and twenty-five alternative testpositions 1010 that are positioned along a two dimensional, fifteen byfifteen grid (labeled 1-15 for convenience of discussion) that isoriented along the X axis and the Y axis. Typically, the number ofdifferent test positions 1010 is greater than two hundred andtwenty-five. For example, in alternative non-exclusive examples, thereare at least approximately twenty-five hundred, five thousand, tenthousand, or twenty thousand test positions 1010. Alternatively, thenumber of different test positions can be less than two hundred andtwenty-five.

It should noted that any of the test positions 1010 can be referred toas a first, second, third, fourth, etc test position 1010. As anon-exclusive example, (i) the test position 1010 at X=1, Y=1 can bereferred to as the first test position; (ii) the test position 1010 atX=1, Y=2 can be referred to as the second test position; and (iii) thetest position 1010 at X=1, Y=3 can be referred to as the third testposition.

Moreover, in the example illustrated in FIG. 10A, for each of thealternative test positions 1010, a center of gravity of the stage is inapproximately the same position along the Z axis, and about the X, Y,and Z axes. Alternatively or additionally, the position of the stagealong the Z axis, and/or about the X, Y, and/or Z axes can also bevaried between some or all of the test positions 1010.

FIGS. 10B and 10C are simplified illustration of an excitation signal.More specifically, FIG. 10B illustrates position versus time for anexcitation signal and FIG. 10C illustrates acceleration versus time forthe excitation signal. As illustrated in FIGS. 10B, 10C, the excitationsignal includes a settling time during which the control of the stageassembly is settling and a measurement time during which useful data canbe obtained. For example, as one example, force commands during themeasurement time can be utilized to generate the compensation map. Asprovided herein, the measurement time can be predetermined.

Referring back to FIG. 9, at step 902, the center of gravity of thestage is moved by the stage mover assembly to a previously unselectedtest position, e.g. the first test position (X1, Y1). With the stage atthe first test position, at step 904, the control system applies an Xaxis excitation signal to the control of the stage mover assembly. The Xaxis excitation signal is designed to cause the stage mover assembly tomove that stage back and forth along the X axis at the selectedamplitude and selected frequency of the X axis excitation signal.

FIG. 11A is a graph that illustrates a first set of excitation signalsthat includes six separate excitation signals 1102, 1104, 1106, 1108,1110, 1112 versus time that are sequentially applied to the control ofthe mover assembly with the stage positioned at the first test position.Subsequently, the set of six separate excitation signals 1102, 1104,1106, 1108, 1110, 1112 are sequentially applied to the control of themover assembly for each subsequent test position of the stage. It shouldbe noted that any of the excitation signals 1102, 1104, 1106, 1108,1110, 1112 can be referred to as a first, second, third, fourth, fifth,or sixth excitation signal.

FIG. 11B is a graph that illustrates the X axis following error versustime that results from the six excitation signals 1102, 1104, 1106,1108, 1110, 1112 with the stage at the first stage position; FIG. 110 isa graph that illustrates the Y axis following error versus time thatresults from the six excitation signals 1102, 1104, 1106, 1108, 1110,1112 with the stage at the first stage position; FIG. 11D is a graphthat illustrates the Z axis following error versus time that resultsfrom the six excitation signals 1102, 1104, 1106, 1108, 1110, 1112 withthe stage at the first stage position; FIG. 11E is a graph thatillustrates the theta X following error versus time that results fromthe six excitation signals 1102, 1104, 1106, 1108, 1110, 1112 with thestage at the first stage position; FIG. 11F is a graph that illustratesthe theta Y following error versus time that results from the sixexcitation signals 1102, 1104, 1106, 1108, 1110, 1112 with the stage atthe first stage position; and FIG. 11G is a graph that illustrates thetheta Z following error versus time that results from the six excitationsignals 1102, 1104, 1106, 1108, 1110, 1112 with the stage at the firststage position.

Moreover, FIG. 11H is a graph that illustrates the X axis force commandsversus time that results from the six excitation signals 1102, 1104,1106, 1108, 1110, 1112 with the stage at the first stage position; FIG.111 is a graph that illustrates the Y axis force commands versus timethat results from the six excitation signals 1102, 1104, 1106, 1108,1110, 1112 with the stage at the first stage position; FIG. 11J is agraph that illustrates the Z axis force commands versus time thatresults from the six excitation signals 1102, 1104, 1106, 1108, 1110,1112 with the stage at the first stage position; FIG. 11K is a graphthat illustrates the theta X moment commands versus time that resultsfrom the six excitation signals 1102, 1104, 1106, 1108, 1110, 1112 withthe stage at the first stage position; FIG. 11L is a graph thatillustrates the theta Y moment commands versus time that results fromthe six excitation signals 1102, 1104, 1106, 1108, 1110, 1112 with thestage at the first stage position; and FIG. 11M is a graph thatillustrates the theta Z moment commands versus time that results fromthe six excitation signals 1102, 1104, 1106, 1108, 1110, 1112 with thestage at the first stage position. It should be noted that theforce/moment commands can be collectively referred to as controlcommands.

Referring back to FIG. 11A, starting at approximately time=0 seconds andcontinuing until approximately time=0.35 seconds, the X axis excitationsignal 1102 is applied. Referring also to FIGS. 11B-11G, after the Xaxis excitation signal 1102 (illustrated in FIG. 11A) is initiallyapplied (at approximately time=0) (i) there is a relatively large X axiserror (as illustrated in FIG. 11B); (ii) there is a small Y axis error(as illustrated in FIG. 110); (iii) there is a moderate Z axis error (asillustrated in FIG. 11D); (iv) there is a small theta X error (asillustrated in FIG. 11E); (v) there is a small theta Y error (asillustrated in FIG. 11F); and (vi) there is a small theta Z axis error(as illustrated in FIG. 11G). Thus, after the X axis excitation signalis initially applied, in addition to the movement of the stage back andforth along the X axis, there is also movement of the stage along the Yand Z axes, and about the X, Y, and Z axes. The time during which eachexcitation signal is initially applied is referred to herein as the“settling time”.

Further, FIGS. 11B-11G illustrate that these following errors arereduced during the time the X axis excitation signal 1102 is appliedbecause of the closed loop control of the control system. Morespecifically, in this example, after approximately time=0.2, thefollowing error that results from the X axis excitation signal for eachdegree of freedom is relatively small. Stated in another fashion,following error that results from the X axis excitation signal for eachdegree of freedom is relatively small near the end of the X excitationcycle. The time near the end of each excitation signal is referred toherein as the “measurement time”.

During the application of the X axis excitation signal, the controlsystem determines the center of gravity force/moment commands thatresult from the X axis excitation signal. Referring to FIGS. 11A, and11H-11M, after the X axis excitation frequency is initially applied (atapproximately time=0) (i) there is a relatively large X axis forcecommand (as illustrated in FIG. 11H); (ii) there is a small Y axis forcecommand (as illustrated in FIG. 11I); (iii) there is a small Z axisforce command (as illustrated in FIG. 11J); (iv) there is a relativelymoderately sized theta X moment command (as illustrated in FIG. 11K);(v) there is a relatively large theta Y moment command (as illustratedin FIG. 11L); and (vi) there is a moderately sized theta Z axis momentcommand (as illustrated in FIG. 11M). Further, because, in this example,the following errors (as illustrated in FIGS. 11B-11G) are relativelysmall after approximately time=0.2, the force/moment commands during themeasurement time of approximately time=0.2 to time=0.35 (near the end ofthe X excitation cycle) are very accurate for the X axis excitationsignal at this test position. As a result thereof, during thismeasurement time, the X axis excitation signal causes the desiredamplitude and frequency movement of the stage back and forth along the Xaxis, and almost no movement of the stage along the Y and Z axes, andabout the X, Y, and Z axes.

Subsequently, in one embodiment, at step 906 of FIG. 9, the controlsystem can calculate an excitation frequency discrete Fourier transform(DFT) value for each of the six center of gravity (CG) force/momentcommands within the measurement time of the X axis excitation signal.This data can be used in the generation of the compensation map asdescribed below.

Next, with the stage still at the first test position, at step 908, thecontrol system applies a Y axis excitation signal to the control of thestage mover assembly. The Y axis excitation signal is designed to causethe stage mover assembly to move that stage back and forth along the Yaxis at the amplitude and frequency of the Y axis excitation signal. Asillustrated in FIG. 11A, starting at approximately 0.45 seconds andcontinuing until approximately 0.85 seconds, the Y axis excitationsignal 1104 is applied. FIGS. 11B-11G illustrate that after the Y axisexcitation signal is initially applied (at approximately time=0.4) (i)there is a relatively large X axis error (as illustrated in FIG. 11B);(ii) there is a relatively large Y axis error (as illustrated in FIG.11C); (iii) there is a small sized Z axis error (as illustrated in FIG.11D); (iv) there is a relatively small theta X error (as illustrated inFIG. 11E); (v) there is a relatively large theta Y error (as illustratedin FIG. 11F); and (vi) there is a relatively small theta Z axis error(as illustrated in FIG. 11G). Further, FIGS. 11B-11G illustrate thatthese errors are generally reduced during the time the Y axis excitationsignal is applied because of the closed loop control of the controlsystem. More specifically, after approximately time=0.6, the followingerror for each degree of freedom is relatively small.

During the application of the Y axis excitation signal, the controlsystem determines the center of gravity force/moment commands thatresult from the Y axis excitation signal. FIGS. 11H-11M illustrate thatafter the Y axis excitation signal is initially applied (atapproximately time=0.45) (i) there is a relatively small X axis forcecommand (as illustrated in FIG. 11H); (ii) there is a relatively large Yaxis force command (as illustrated in FIG. 11I); (iii) there is a smallsized Z axis force command (as illustrated in FIG. 11J); (iv) there is arelatively large sized theta X moment command (as illustrated in FIG.11K); (v) there is a moderately sized theta Y moment command (asillustrated in FIG. 11L); and (vi) there is a small sized theta Z axismoment command (as illustrated in FIG. 11M). Further, because, in thisexample, the following errors (as illustrated in FIGS. 11B-11G) arerelatively small after approximately time=0.6, the force and momentcommands during the measurement time of approximately time=0.6 totime=0.75 (near the end of the Y excitation cycle) are very accurate forthe Y axis excitation signal at this test position. As a result thereof,during this measurement time, the Y axis excitation signal causes thedesired amplitude and frequency movement of the stage back and forthalong the Y axis, and almost no movement of the stage along the X and Zaxes, and about the X, Y, and Z axes.

Subsequently, in one embodiment, at step 910 of FIG. 9, the controlsystem can calculate an excitation frequency discrete Fourier transform(DFT) value for each of the six center of gravity (CG) force/momentcommands within the measurement time of the Y axis excitation signal.

Next, with the stage still at the first test position, at step 912, thecontrol system applies a Z axis excitation signal to the control of thestage mover assembly. The Z axis excitation signal is designed to causethe stage mover assembly to move that stage back and forth along the Zaxis at the amplitude and frequency of the Z axis excitation signal. Asillustrated in FIG. 11A, starting at approximately time=0.8 seconds, theZ axis excitation signal 1106 is applied. FIGS. 11B-11G illustrate therespective following errors that result from the application of the Zaxis excitation signal. Further, FIGS. 11B-11G illustrate that theseerrors are generally reduced during the time the Z axis excitationsignal is applied because of the closed loop control of the controlsystem. More specifically, the following error for each degree offreedom is relatively small near the end of the application of the Zaxis excitation signal.

During the application of the Z axis excitation signal, the controlsystem determines the center of gravity force/moment commands thatresult from the Z axis excitation signal. FIGS. 11H-11M illustrate theforce and moment commands that result from the Z axis excitation signal.Further, because, the following errors (as illustrated in FIGS. 11B-11G)are relatively small near the end of the Z axis excitation cycle, theforce and moment commands during this measurement time are very accuratefor the Z axis excitation signal at this test position.

Subsequently, in one embodiment, at step 914 of FIG. 9, the controlsystem can calculate an excitation frequency discrete Fourier transform(DFT) value for each of the six center of gravity (CG) force/momentcommands within the measurement time of the Z axis excitation signal.

Next, with the stage still at the first test position, at step 916, thecontrol system applies a theta X excitation signal to the control of thestage mover assembly. The theta X excitation signal is designed to causethe stage mover assembly to move that stage back and forth about the Xaxis at the amplitude and frequency of the theta X excitation signal.FIGS. 11B-11G illustrate the respective following errors that resultfrom the application of the theta X excitation signal. Further, FIGS.11B-11G illustrate that these errors are generally reduced during thetime the theta X excitation signal is applied because of the closed loopcontrol of the control system. More specifically, the following errorfor each degree of freedom is relatively small near the end of theapplication of the theta X excitation signal.

During the application of the theta X excitation signal, the controlsystem determines the center of gravity force/moment commands thatresult from the theta X excitation signal. FIGS. 11H-11M illustrate theforce and moment commands that result from the theta X excitationsignal. Further, because, in this example, the following errors (asillustrated in FIGS. 11B-11G) are relatively small near the end of thetheta X excitation cycle, the force and moment commands during thismeasurement time are very accurate for the theta X excitation signal atthis test position.

Subsequently, in one embodiment, at step 918 of FIG. 9, the controlsystem can calculate an excitation frequency discrete Fourier transform(DFT) value for each of the six center of gravity (CG) force/momentcommands within the measurement time of the theta X excitation signal.

Next, with the stage still at the first test position, at step 920, thecontrol system applies a theta Y excitation signal to the control of thestage mover assembly. The theta Y excitation signal is designed to causethe stage mover assembly to move that stage back and forth about the Yaxis at the amplitude and frequency of the theta Y excitation signal.FIGS. 11B-11G illustrate the respective following errors that resultfrom the application of the theta Y excitation signal. Further, FIGS.11B-11G illustrate that these errors are generally reduced during thetime the theta Y excitation signal is applied because of the closed loopcontrol of the control system. More specifically, the following errorfor each degree of freedom is relatively small near the end of theapplication of the theta Y excitation signal.

During the application of the theta Y excitation signal, the controlsystem determines the center of gravity force/moment commands thatresult from the theta Y excitation signal. FIGS. 11H-11M illustrate theforce and moment commands that result from the theta Y excitationsignal. Further, because, in this example, the following errors (asillustrated in FIGS. 11B-11G) are relatively small near the end of thetheta Y excitation cycle, the force and moment commands during thismeasurement time are very accurate for the theta Y excitation signal atthis test position.

Subsequently, in one embodiment, at step 922 of FIG. 9, the controlsystem can calculate an excitation frequency discrete Fourier transform(DFT) value for each of the six center of gravity (CG) force/momentcommands within the measurement time of the theta Y excitation signal.

Next, with the stage still at the first test position, at step 924, thecontrol system applies a theta Z excitation signal to the control of thestage mover assembly. The theta Z excitation signal is designed to causethe stage mover assembly to move that stage back and forth about the Zaxis at the amplitude and frequency of the theta Z excitation signal.FIGS. 11B-11G illustrate the respective following errors that resultfrom the application of the theta Z excitation signal. Further, FIGS.11B-11G illustrate that these errors are generally reduced during thetime the theta Z excitation signal is applied because of the closed loopcontrol of the control system. More specifically, the following errorfor each degree of freedom is relatively small near the end of theapplication of the theta Z excitation signal.

During the application of the theta Z excitation signal, at step 926,the control system determines the center of gravity force/momentcommands that result from the theta Z excitation signal. FIGS. 11H-11Millustrate the force and moment commands that result from the theta Zexcitation signal. Further, because, in this example, the followingerrors (as illustrated in FIGS. 11B-11G) are relatively small near theend of the theta Z excitation cycle, the force and moment commandsduring this measurement time are very accurate for the theta Zexcitation signal at this test position.

Subsequently, in one embodiment, at step 926 of FIG. 9, the controlsystem can calculate an excitation frequency discrete Fourier transform(DFT) value for each of the six center of gravity (CG) force/momentcommands within the measurement time of the theta Z excitation signal.

Next, at step 928, the control system evaluates if all of the testpositions have been selected. If not, the center of gravity of the stageis moved to the next test position (e.g. the second test position), andthe X, Y, Z, theta X, theta Y, and theta Z excitation signals aresequentially applied and the six force/moment commands are determinedfor each of the six excitation signals. Subsequently, the center ofgravity of the stage is moved to the next test position (e.g. the thirdtest position), and the X, Y, Z, theta X, theta Y, and theta Zexcitation signals are sequentially applied and the six force/momentcommands are determined for each of the six excitation signals.

This process is repeated until the X, Y, Z, theta X, theta Y, and thetaZ excitation signals are sequentially applied and the resulting sixforce/moment commands are determined for each of the six excitationsignals for each of the test positions. After that is done, thecompensation map can be generated at step 930.

The selected magnitude and selected frequency of each excitation signal1101, 1104, 1106, 1108, 1110, 1112 can be varied to suit the designrequirements of the stage assembly. For example, the magnitude of eachexcitation signal can cause a position excitation of approximately onehundred microns along the X, Y or Z axis, or rotation of approximatelyone hundred microrads about the X, Y, or Z axis. Alternatively, one ormore of the excitation signals can cause a position excitation ofgreater than or lesser than these amounts. In certain embodiments, thefrequency of the excitation signal is lower than the closed loopbandwidth of the control system. For example, if system has a closedloop bandwidth of approximately one hundred hertz, the excitationfrequency can be selected to be approximately fifty hertz. Asalternative, non-exclusive examples, the excitation frequency can be asine wave of approximately 20, 40, 60, 80, 100, 200, 300, 400, or 500hertz.

Further, the duration of the excitation signal 1101, 1104, 1106, 1108,1110, 1112 should be long enough to achieve good force/moment commands.As non-exclusive examples, each excitation cycle can have a duration ofapproximately 0.25, 0.3, 0.4, 0.5, or 0.6 seconds. However, the durationcan be greater to less than these amounts.

Moreover, it should be noted that the present compensation method canutilize less than six excitation signals per test position. For example,the method can utilize (i) just three (e.g. the X, Y, and Z axes) of theexcitation signals at each test position, (ii) just two (e.g. the X, andY axes) of the excitation signals at each test position, or (iii) justone (e.g. the X axis) of the excitation signals at each test position.

Additionally, referring to FIG. 10, it should be noted that the order inwhich the test positions 1010 are evaluated can be varied. In FIG. 10,arrow 1012 illustrates one, non-exclusive example of the order in whichthe test positions 1010 can evaluated. In this example, the testpositions 1010 with an X value of 1 are sequentially tested moving fromY=1 to Y=15. Next, the second column are sequentially tested, X=2 andmoving from Y=15 to Y=1. This pattern is repeated for the entire grid.Alternatively, another order can be utilized.

FIG. 12 is a simplified control block diagram of a control system 1224that can be used to apply the sequential excitation signals, determineforce/moment commands for each of the test positions, and generate theinformation for the compensation map for the mover assembly of FIG. 2A.With this design, the control system 1224 is able to make the feedbackof the system approximately perfect at the selected frequency of theexcitation signals. In FIG. 12, the control block diagram 1224 issomewhat similar to the control block diagram illustrated in FIG. 3.However, in FIG. 12, the control system 1224 includes an accelerationfeedforward block 1270, an excitation signal block 1272, and a cancellerblock 1274.

In FIG. 12 (similar to FIG. 3), (i) “m” represents the measured, actualmomentary, position; and (ii) “e” represents a following error. Further,starting at the left side of the control block diagram 1224, theexcitation signal 1272 is fed into the control system 624 along with themeasured position “m”. Next, the control system 1224 determines thefollowing error “e”. Subsequently, the following error “e” is fed into afeedback control 1252 of the control system 1224. Further, if one ormore of the movers do not push through the center of gravity of thestage, the control system 1224 can include a center of gravity forcecompensation map 1254 that compensates for this. Next, a forcedistribution 1256 determines the force commands for each of the moversnecessary to correct the following error. Subsequently, the movercommutations 1258 are utilized to determine the currents that movers.Next, at block 1260, the movers move the stage.

In the design illustrated in FIG. 12, the acceleration feedforward block1270 is used to reduce the transient delay in the movement of the stage.During movement of the stage, the desired trajectory of the stage andthe mass of the stage are known. The feedforward block 1270 is used toinject a force proportional to desired acceleration that is needed tomove the stage moving towards its desired destination. This reduces thetransient delay of the system.

The excitation signal block 1272 is used to sequentially apply theexcitation signals (e.g. the X, Y, Z, theta X, theta Y, and theta Zexcitation signals) to the control of the mover assembly for each of thetest positions. In one embodiment, the excitation signals can berepresented by the following equations:

x_(d)+A(t)sin(wt) for the X excitation signal;  Equation (7)

y_(d)+A(t)sin(wt) for the Y excitation signal;  Equation (8)

z_(d)+A(t)sin(wt) for the Z excitation signal;  Equation (9)

Tx_(d)+A(t)sin(wt) for the theta X excitation signal;  Equation (10)

Ty_(d)+A(t)sin(wt) for the theta Y excitation signal;  Equation (11)

Tz_(d)+A(t)sin(wt) for the theta Z excitation signal.  Equation (12)

In these equations, (i) x_(d) is the stage X axis reference positionbefore excitations; (ii) y_(d) is the stage Y axis reference positionbefore excitations; (iii) z_(d) is stage Z axis reference positionbefore excitations; (iv) Tx_(d) is the stage theta X axis referenceposition before excitations; (v) Ty_(d) is the stage theta Y axisreference position before excitations; (vi) Tz_(d) is the stage theta Zaxis reference position before excitations; (vii) A is the positionexcitation magnitude; and (viii) w is the position excitation frequency.

Further, for each test position, the canceller 1274 is used to determinethe six force/moment commands for each of the six excitation signals. Asprovided herein, the canceller 1274 is applied to the feedback control1252 for each degree of freedom to achieve nearly perfect control forceat the excitation frequency. The design of the canceller 1274 can bevaried pursuant to the teachings provided herein. In one non-exclusiveembodiment, the canceller 1274 is a filter that is approximatelyopposite to a notch filter. In one embodiment, the canceller 1274 is afixed parameter transfer function that is described by the followingequations:

$\begin{matrix}{{C_{C}(s)} = {1 + {g_{c} \cdot \frac{{{{Cos}\left( \theta_{c} \right)} \cdot s} + {{\sin \left( \theta_{c} \right)} \cdot w_{c}}}{s^{2} + w_{c}^{2}}}}} & {{Equation}\mspace{14mu} (13)} \\{{C_{C}(s)} = \frac{s^{2} + {g_{c}{{{Cos}\left( \theta_{c} \right)} \cdot s}} + {g_{c}{{\sin \left( \theta_{c} \right)} \cdot w_{c} \cdot w_{c}^{2}}}}{s^{2} + w_{c}^{2}}} & {{Equation}\mspace{14mu} (14)}\end{matrix}$θ_(C) =∠T _(closed-loop)(w _(c))  Equation (15)

g _(C)=2d _(c) w _(c)  Equation (16)

In these equations, (i) C_(C) is the transfer function of the canceller;(ii) is the complex argument for Laplace transform; (iii) g_(C) is thecanceller gain; (iv) θ_(C) is the canceller phase; (v) w_(C) is thecanceller frequency, which is selected as same as the excitationfrequency w_(C)=w; (vi) ∠T_(closed-loop)(w_(c)) is the phase ofclosed-loop system at the canceller frequency; and (vii) d_(C) isnumerator damping ratio of the canceller transfer function.

As provided above, for each test position, the information obtained nearthe end (during the measurement time) of each excitation cycle regardingthe force/moment commands for each excitation signal can be subsequentlyused to control the stage with improved accuracy. For each testposition, (i) the X, Y, Z, Tx, Ty, and Tz force/moment commands near theend (during the measurement time) of the X excitation cycle can bereferred to as a X set of control commands, (ii) the X, Y, Z, Tx, Ty,and Tz force/moment commands near the end (during the measurement time)of the Y excitation cycle can be referred to as a Y set of controlcommands, (iii) the X, Y, Z, Tx, Ty, and Tz force/moment commands nearthe end (during the measurement time) of the Z excitation cycle can bereferred to as a Z set of control commands, (iv) the X, Y, Z, Tx, Ty,and Tz force/moment commands near the end (during the measurement time)of the theta X excitation cycle can be referred to as a theta X set ofcontrol commands, (v) the X, Y, Z, Tx, Ty, and Tz force/moment commandsnear the end (during the measurement time) of the theta Y excitationcycle can be referred to as a theta Y set of control commands, and (vi)the X, Y, Z, Tx, Ty, and Tz force/moment commands near the end (duringthe measurement time) of the theta Z excitation cycle can be referred toas a theta Z set of control commands. Further, any of these sets can bereferred to as a first, second, third, fourth, fifth, or sixth set ofcontrol commands.

Additionally, the information from the sets of control commands can beused in a number of different fashions. For example, the sets of controlcommands for each test position can be used to generate a compensationmap that is used to subsequently control the stage with improvedaccuracy. Alternatively, the end of cycle force/moment commands can beused to generate motor ripple and side force information that can beused to subsequently control the stage.

In the specific example described in detail herein, for each testposition, there are six separate excitation signals (namely X, Y, Z, Tx,Ty, and Tz excitation signals), and each excitation signal has sixcorresponding force/moment commands (X, Y, Z force commands and Tx, Ty,and Tz moment commands). This results in thirty six sets of controlcommands for each test position. Further, this information can becomplied into a six by six matrix for each test position.

As provided above, in one non-exclusive embodiment, informationregarding the force/moment commands for each test position can be usedto generate a compensation map for the mover assembly. The actualprocedure used to generate the compensation map can be varied. In oneembodiment, a discrete Fourier transform (DFT) is used to transform thesix by six matrix of control commands for each test position into acompensation map for the mover assembly. Thus, the discrete Fouriertransform is used to convert force/moment commands to force constant.Stated in another fashion, a single frequency Discrete Fourier Transformis performed on all six axis force commands for good signal quality atthe test excitation frequency. In one embodiment, the frequency of theDiscrete Fourier Transform is the same as the frequency of theexcitation signal. With this design, the good quality force/momentcommand information can be used to generate a very accurate and cleanripple/side force compensation map. The equation below illustrates thecomputation of CG force compensation ratios from X axis to all 6 axes atevery test position (x_(i), y_(j)). Similar equations may be derived forCG force command compensation ratios from the other five axes to all 6axes.

$\begin{bmatrix}{K_{XX}\left( {x_{i},y_{j}} \right)} \\{K_{YX}\left( {x_{i},y_{j}} \right)} \\{K_{ZX}\left( {x_{i},y_{j}} \right)} \\{K_{TxX}\left( {x_{i},y_{j}} \right)} \\{K_{TyX}\left( {x_{i},y_{j}} \right)} \\{K_{TzX}\left( {x_{i},y_{j}} \right)}\end{bmatrix} = {{real}\left\lbrack {\frac{1}{\frac{1}{NM}{\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{M}{U_{x}\left( {x_{i},y_{j}} \right)}}}} \cdot \begin{bmatrix}{U_{X}\left( {x_{i},y_{j}} \right)} \\{U_{Y}\left( {x_{i},y_{j}} \right)} \\{U_{Z}\left( {x_{i},y_{j}} \right)} \\{U_{Tx}\left( {x_{i},y_{j}} \right)} \\{U_{Ty}\left( {x_{i},y_{j}} \right)} \\{K_{Tz}\left( {x_{i},y_{j}} \right)}\end{bmatrix}} \right\rbrack}$Equation (17)

In this equation (i) K_(XX)(x_(i), y_(j)) represents the force commandcompensation ratio from X axis to X axis; (ii) K_(YX)(x_(i), y_(j))represents the force command compensation ratio from X axis to Y axis;(iii) K_(ZX)(x_(i), y_(j)) represents the force command compensationratio from X axis to Z axis; (iv) K_(TxX)(x_(i), y_(i)) represents theforce command compensation ratio from X axis to theta X axis; (v)K_(TyX)(x_(i), y_(j)) represents the force command compensation ratiofrom X axis to theta Y axis; (vi) K_(TzX)(x_(i), y_(j)) represents theforce command compensation ratio from X axis to theta Z axis; (vii)U_(X)(x_(i), y_(j)) is the X force command DFT at position (x_(i),y_(j)); (viii) U_(Y)(x_(i), y_(j)) is the Y force command DFT atposition (x_(i), y_(j)); (ix) U_(Z) (x_(i), y_(j)) is the Z forcecommand DFT at position (x_(i), y_(j)); (x) U_(Tx)(x_(i), y_(j)) is thetheta X force command DFT at position (x_(i), y_(j)); (xi) U_(Ty)(x_(i),y_(j)) is the theta Y force command DFT at position (x_(i), y₁); (xii)U_(Tz)(x_(i), y_(j)) is the theta Z force command DFT at position(x_(i), y_(j)); (xiii) N is the number of calibration positions alongstage X axis; and (xiv) M is the number of calibration positions alongstage Y axis.

With this design, the ratios of all-axes force command DFT arecalculated, and the excitation-axis force commands DFT are averaged andnormalized at all test positions.

Further, in certain embodiments, a two dimensional fast Fouriertransform (or other method) can be used on the compensation map toremove potential non-smooth offset between two measurement columns,caused by hysteresis of the stage electrical cables and cooling tubes.

FIG. 13A is a plot that illustrates one non-exclusive example of theresulting compensation ratio for the X axis excitation signal for the Xaxis for the plurality of test positions; FIG. 13B is a plot thatillustrates one non-exclusive example of the resulting compensationratio for the X axis excitation signal for the Y axis for the pluralityof test positions; FIG. 13C is a plot that illustrates one non-exclusiveexample of the resulting compensation ratio for the X axis excitationsignal for the Z axis for the plurality of test positions; FIG. 13D is aplot that illustrates one non-exclusive example of the resultingcompensation ratio for the X axis excitation signal for the theta X forthe plurality of test positions; FIG. 13E is a plot that illustrates onenon-exclusive example of the resulting compensation ratio for the X axisexcitation signal for the theta Y for the plurality of test positions;and FIG. 13F is a plot that illustrates one non-exclusive example of theresulting compensation ratio for the X axis excitation signal for thetheta Z for the plurality of test positions. In each Figure, the X and Yaxes represents X and Y test positions of the stage, and the Z axisrepresents the corresponding, calculated compensation value for eachtest position.

The FIG. 13A plot can be generated utilizing the DFT on the X forcecommands near the end of the X excitation cycle for the plurality oftest positions; the FIG. 13B plot can be generated utilizing the DFT onthe Y force commands near the end of the X excitation cycle for theplurality of test positions; the FIG. 13C plot can be generatedutilizing the DFT on the Z force commands near the end of the Xexcitation cycle for the plurality of test positions; the FIG. 13D plotcan be generated utilizing the DFT on the theta X moment commands nearthe end of the X excitation cycle for the plurality of test positions;the FIG. 13E plot can be generated utilizing the DFT on the theta Ymoment commands near the end of the X excitation cycle for the pluralityof test positions; and the FIG. 13F plot can be generated utilizing theDFT on the theta Z moment commands near the end of the X excitationcycle for the plurality of test positions.

In this embodiment, the X sets of control commands (that result from theX excitation cycle) for each test position is used to generate sixseparate X plots (illustrated in FIGS. 13A-13F) that form part of thecompensation map. Further, it should be noted that six separate plotscan be generated for each of the other five (Y, Z, Tx, Ty, Tz)excitation signals. More specifically, (i) the Y sets of controlcommands for each test position can be used to generate six separate Yplots; (ii) the Z sets of control commands for each test position can beused to generate six separate Z plots; (iii) the theta X sets of controlcommands for each test position can be used to generate six separatetheta X plots; (iv) the theta Y sets of control commands for each testposition can be used to generate six separate theta Y plots; and (v) thetheta Z sets of control commands for each test position can be used togenerate six separate theta Z plots.

FIG. 14A is a plot that illustrates one, non-exclusive example of aresulting force compensation map 1402 for all of the test positions andall of the excitation signals. In this example, the compensation map isa six by six force compensation map 1402 that includes thirty six plots,namely (i) six X plots (the left most column 1404 of the compensationmap 1402) that result from the application of the X excitation signals;(ii) six Y plots (the second from the left column 1406 of thecompensation map 1402) that result from the application of the Yexcitation signals; (iii) six Z plots (the third from the left column1408 of the compensation map 1402) that result from the application ofthe Z excitation signals; (iv) six Tx plots (the fourth from the leftcolumn 1410 of the compensation map 1402) that result from theapplication of the theta X excitation signals; (v) six Ty plots (thefifth from the left column 1412 of the compensation map 1402) thatresult from the application of the theta Y excitation signals; and (vi)six Tz plots (the right most column 1414 of the compensation map 1402)that result from the application of the theta Z excitation signals.

FIG. 14B is an enlarged illustration of a portion of the compensationmap of FIG. 14A. More specifically, FIG. 14B illustrates the To Ty FromTz plot. This plot represents the force compensation plot for the thetaY that results from the application of the theta Z excitation signals.In FIG. 14B, each of test positions has a Y position value and an Xposition value. Further, for each test position has a force compensationvalue that is represented a shade of gray in FIG. 14B. In this Figure,the scale for each shade of gray is illustrated along the right side ofthe plot.

Further, it should be noted that similar to the plot illustrated in FIG.14B, for each plot illustrated in FIG. 14A, the X axis represents thelocation along the X axis of the test position, the Y axis representsthe location along the Y axis of the test position, and shade representsthe associated compensation value.

FIG. 15A is a simplified control block diagram of a control system 1524that can use the compensation map 1402 (illustrated in FIG. 14A) tocontrol the mover assembly to position the stage with improved accuracy.In FIG. 15A, the control block diagram 1524 is somewhat similar to thecontrol block diagram illustrated in FIG. 3. However, in FIG. 15A, thecontrol system 1524 includes the feedforward control block 1570 that issimilar to but more general than the corresponding block described aboveand illustrated in FIG. 12, a first time-ahead position trajectory block1580, and a second time-ahead position trajectory block 1582.

In FIG. 15A (similar to FIG. 3), (i) “r” represents a desired position;(ii) “m” represents the measured, actual momentary, position; and (iii)“e” represents a following error. Further, starting at the left side ofthe control block diagram 1254, the desired position is fed into thecontrol system 1224 along with the measured position “m”. Next, thecontrol system 1224 determines the following error “e”. Subsequently,the following error “e” is fed into a feedback control 1552. In oneembodiment, the identified compensation map 1402 (illustrated in FIG.14) can be used in the CG force compensation 1554 to compensate formotor force ripple, side forces and other cross-axes couplings that havebeen also picked up by the calibration procedure. Next, a forcedistribution 1556 determines the force commands for each of the moversnecessary to correct the following error. Subsequently, the movercommutations 1558 are utilized to determine the currents that movers.Next, at block 1560, the movers move the stage.

In the design illustrated in FIG. 15A, feedforward block 1570 is used toprovide approximately the right force command for the movement of thestage. In certain designs, the feedforward block 1570 can be anacceleration feedforward. Alternatively, the feedforward can be moregeneral.

Further, to accommodate the system time delay generally embedded in thecontrol system, time ahead position trajectory can be used in the CGforce compensate map 1554 and motor commutation 1558 such that theiroutputs will happen at the correct time. The first time-ahead positiontrajectory 1580 is fed into the center of gravity force compensation1554. Additionally, the information from the compensation map is used inthe center of gravity force compensation 1554. The first time-aheadposition trajectory 1580 is used to look where the stage position isgoing to be when the current is directed to the mover assembly. Thus,with the time-ahead position trajectory 1580, the correct compensationratio from the compensation map is utilized for when the current isactually directed to the mover assembly.

Moreover, the second time-ahead position trajectory 1582 is fed into themotor commutation 1558. The second time-ahead position trajectory 1582makes the motor currents have the correct phases.

FIG. 15B illustrates a six by six force compensation matrix. As providedherein, in certain embodiments, the generated compensation map 1402 (oneexample illustrated in FIG. 14A) is used in the CG force compensationblock 1554 (illustrated in FIG. 15A) as a six by six, two dimensionallook-up table. Utilizing interpolation methods, the look-up tableprovides six by six compensation matrix in FIG. 15B for every stageposition.

In FIG. 15B (i) “u_(x)”—represents CG force command along the X axis;(ii) “u_(y)”—CG force command along the Y axis; (iii) “u_(z)”—representsthe CG force command along the Z axis; (iv) “u_(tx)”—represents CG forcecommand along the Theta-X axis; (v) “u_(tx)”—represents the CG forcecommand along the Theta-Y axis; (vii) “u_(tz)”—represents the CG forcecommand along the Theta-Z axis; (viii) “k_(XX)”—represents the forcecommand compensation ratio from X axis to X axis; (ix)“k_(YX)”—represents the force command compensation ratio from X axis toY axis; (x) “k_(ZX)”—represents the force command compensation ratiofrom X axis to Z axis; (x) “k_(TxX)”—represents the force commandcompensation ratio from X axis to Theta-X axis; (xi)“k_(TyX)”—represents the force command compensation ratio from X axis toTheta-Y axis; (xii) “k_(TzX)”—represents the force command compensationratio from X axis to Theta-Z axis; (xiii) “Xr”—represents the X axisreference position; (xiv) “Yr”—represents the Y axis reference position;(xv) “t” represents time; (xvi) “td” represents the system delay; and(xvii) “Xr(t+td)”—represents the time-ahead X axis reference position toaccommodate the system time delay.

The formula used in the motor commutation 1558 for the XZ and YZ moversto transform the mover horizontal and vertical force commands to thethree-phase current commands are described in Equations (1), (2), (3)and (4).

FIG. 16 is a graph that includes (i) dashed line 1602 that representsthe X position of the stage versus time, and (ii) solid line 1604 thatrepresents the Y position of the stage versus time during movement ofthe stage. FIG. 17A is a graph that includes (i) dashed line 1702 thatrepresents the X following error versus time without the compensationprovided herein, and (ii) solid line 1704 that represents the Xfollowing error versus time with the compensation provided for themovement illustrated in FIG. 16. FIG. 17B is a graph that includes (i)dashed line 1706 that represents the Y following error versus timewithout the compensation provided herein, and (ii) solid line 1708 thatrepresents the Y following error versus time with the compensationprovided for the movement illustrated in FIG. 16. FIG. 17C is a graphthat includes (i) dashed line 1710 that represents the Z following errorversus time without the compensation provided herein, and (ii) solidline 1712 that represents the Z following error versus time with thecompensation provided for the movement illustrated in FIG. 16. FIG. 17Dis a graph that includes (i) dashed line 1714 that represents the Txfollowing error versus time without the compensation provided herein,and (ii) solid line 1716 that represents the Tx following error versustime with the compensation provided for the movement illustrated in FIG.16. FIG. 17E is a graph that includes (i) dashed line 1718 thatrepresents the Ty following error versus time without the compensationprovided herein, and (ii) solid line 1720 that represents the Tyfollowing error versus time with the compensation provided for themovement illustrated in FIG. 16. FIG. 17F is a graph that includes (i)dashed line 1722 that represents the Tz following error versus timewithout the compensation provided herein, and (ii) solid line 1724 thatrepresents the Tz following error versus time with the compensationprovided for the movement illustrated in FIG. 16. These Figuresillustrate that the stage following errors in all six degrees of freedomare highly reduced by use of the compensation methods disclosed herein.

It should also be noted even with the CG force compensation providedherein, that there can still be some smaller residual stage followingerrors during stepping and scanning motion due to other disturbancessuch as electrical cables, cooling tubes, etc.

FIG. 18A is a map 1802 that illustrates the residual force compensationratios with the application of the center of gravity force compensation.More specifically, with the CG force compensation applied, the samecalibration procedure (using multiple excitation signals at multiplemeasurement positions) can be used measure the residual forcecompensation ratios again to verify the effectiveness of the appliedcompensation. A comparison of the map 1802 provided in FIG. 18A withthat in FIG. 14A (without compensation), illustrates the force couplingsamong axes after compensation are much less. The scales are the same inFIGS. 18A and 14A. Thus, FIG. 18A illustrates the effectiveness of thecompensation for motor force ripples and side forces.

FIG. 18B is an enlarged illustration of a portion of the map of FIG.18A. More specifically, FIG. 18B illustrates the To Ty From Tz plot.This plot represents the plot for the theta Y that results from theapplication of the theta Z excitation signals. In FIG. 18B, each of testpositions has a Y position value and an X position value. Further, foreach test position has a force compensation value that is represented ashade of gray in FIG. 18B. In this Figure, the scale for each shade ofgray is illustrated along the right side of the plot. It should be notedthat for the values in this plot, the shade is approximately the sameand is approximately equal to zero.

Further, it should be noted that similar to the plot illustrated in FIG.18B, for each plot illustrated in FIG. 18A, the X axis represents thelocation along the X axis of the test position, the Y axis representsthe location along the Y axis of the test position, and shade representsthe associated compensation value.

Semiconductor devices can be fabricated using the above describedsystems, by the process shown generally in FIG. 19A. In step 1901 thedevice's function and performance characteristics are designed. Next, instep 1902, a mask (reticle) having a pattern is designed according tothe previous designing step, and in a parallel step 1903 a wafer is madefrom a silicon material. The mask pattern designed in step 1902 isexposed onto the wafer from step 1903 in step 1904 by a photolithographysystem described hereinabove in accordance with the present invention.In step 1905, the semiconductor device is assembled (including thedicing process, bonding process and packaging process), finally, thedevice is then inspected in step 1906.

FIG. 19B illustrates a detailed flowchart example of the above-mentionedstep 1904 in the case of fabricating semiconductor devices. In FIG. 19B,in step 1911 (oxidation step), the wafer surface is oxidized. In step1912 (CVD step), an insulation film is formed on the wafer surface. Instep 1913 (electrode formation step), electrodes are formed on the waferby vapor deposition. In step 1914 (ion implantation step), ions areimplanted in the wafer. The above mentioned steps 1911-1914 form thepreprocessing steps for wafers during wafer processing, and selection ismade at each step according to processing requirements.

At each stage of wafer processing, when the above-mentionedpreprocessing steps have been completed, the following post-processingsteps are implemented. During post-processing, first, in step 1915(photoresist formation step), photoresist is applied to a wafer. Next,in step 1916 (exposure step), the above-mentioned exposure device isused to transfer the circuit pattern of a mask (reticle) to a wafer.Then in step 1917 (developing step), the exposed wafer is developed, andin step 1918 (etching step), parts other than residual photoresist(exposed material surface) are removed by etching. In step 1919(photoresist removal step), unnecessary photoresist remaining afteretching is removed. Multiple circuit patterns are formed by repetitionof these preprocessing and post-processing steps.

It is to be understood that movers disclosed herein are merelyillustrative of the presently preferred embodiments of the invention andthat no limitations are intended to the details of construction ordesign herein shown other than as described in the appended claims.

1. A method for controlling a mover assembly that moves and positions astage relative to a stage base, the method comprising the steps of:controlling the mover assembly with a control system to position thestage at a first test position; applying a first excitation signal withthe control system to the mover assembly with the stage at the firsttest position; and determining a first set of control commands for thefirst excitation signal.
 2. The method of claim 1 further comprising thesteps of applying a second excitation signal with the control system tothe mover assembly with the stage at the first test position, anddetermining a second set of control commands for the second excitationsignal.
 3. The method of claim 2 further comprising the step ofcontrolling the mover assembly with the control system utilizinginformation from the sets of control commands.
 4. The method of claim 2further comprising the steps of generating a compensation map from thefirst set of control commands and the second set of control commands,and controlling the mover assembly with the control system utilizinginformation from the compensation map.
 5. The method of claim 2 furthercomprising the steps of moving the stage to a second test position thatis different than the first test position, applying a third excitationsignal with the control system to the mover assembly with the stage atthe second test position; and determining a third set of controlcommands for the third excitation signal.
 6. The method of claim 5further comprising the step of controlling the mover assembly with thecontrol system utilizing information from the sets of control commands.7. The method of claim 1 further comprising the steps of moving thestage to a second test position that is different than the first testposition, applying a second excitation signal with the control system tothe mover assembly with the stage at the second test position; anddetermining a second set of control commands for the second excitationsignal.
 8. The method of claim 7 further comprising the step ofcontrolling the mover assembly with the control system utilizinginformation from the sets of control commands.
 9. A method ofcompensating the control of a stage assembly, the method comprising thesteps of determining (i) the first set of control commands and thesecond set of control commands by the method of claim 7, (ii) generatinga compensation map from the first set of control commands and the secondset of control commands, and (iii) controlling the mover assembly withthe control system utilizing information from the compensation map. 10.A method for controlling a mover assembly that moves and positions astage relative to a stage base, the method comprising the steps of:controlling the mover assembly with a control system to position thestage at a first test position; applying a first set of excitationsignals with the control system to the mover assembly with the stage atthe first test position; determining a first set of control commands foreach of the excitation signals of the first set; controlling the moverassembly with the control system to position the stage at a second testposition that is different than the first test position; applying asecond set of excitation signals with the control system to the moverassembly with the stage at the second test position; determining asecond set of control commands for each of the excitation signals of thesecond set; and generating a compensation map from the first set ofcontrol commands and the second set of control commands, and controllingthe mover assembly with the control system utilizing information fromthe compensation map.
 11. A mover assembly that moves and positions astage relative to a stage base, the mover assembly comprising: a moverthat moves and positions the stage relative to the stage base; and acontrol system that controls the mover, the control system (i) directingcurrent to the mover to position the stage at a first test position;(ii) applying a first excitation signal to the mover with the stage atthe first test position; and (iii) determining a first set of controlcommands for the first excitation signal.
 12. The mover assembly ofclaim 11 wherein the control system applies a second excitation signalto the mover with the stage at the first test position, and determines asecond set of control commands for the second excitation signal.
 13. Themover assembly of claim 12 wherein the control system controls the moverassembly utilizing information from the sets of control commands. 14.The mover assembly of claim 12 wherein the control system generates acompensation map from the first set of control commands and the secondset of control commands, and controls the mover utilizing informationfrom the compensation map.
 15. The mover assembly of claim 12 whereinthe control system (i) directs current to the mover to move the stage toa second test position that is different than the first test position,(ii) applies a third excitation signal with the control system to themover assembly with the stage at the second test position; and (iii)determines a third set of control commands for the third excitationsignal.
 16. The mover assembly of claim 15 wherein the control systemcontrols the mover utilizing information from the sets of controlcommands.
 17. The mover assembly of claim 11 wherein the control system(i) directs current to the mover to move the stage to a second testposition that is different than the first test position, (ii) applies asecond excitation signal to the mover with the stage at the second testposition, and (iii) determines a second set of control commands for thesecond excitation signal.